Let's pick a sample table on my machine:

mysql> show create table weisci_jaws_staging2.users\G
*************************** 1. row ***************************
       Table: users
Create Table: CREATE TABLE `users` (
  `id` int(11) NOT NULL AUTO_INCREMENT,
  `username` varchar(32) NOT NULL DEFAULT '',
  `passwd` varchar(32) NOT NULL DEFAULT '',
  `user_type` tinyint(4) DEFAULT '2',
  `recovery_key` varchar(48) DEFAULT NULL,
  `name` varchar(255) DEFAULT NULL,
  `email` varchar(255) DEFAULT NULL,
  `url` varchar(255) DEFAULT NULL,
  `timezone` varchar(5) DEFAULT NULL,
  `language` varchar(5) DEFAULT NULL,
  `theme` varchar(24) DEFAULT NULL,
  `editor` varchar(24) DEFAULT NULL,
  `last_login` datetime DEFAULT NULL,
  `createtime` datetime DEFAULT NULL,
  `updatetime` datetime DEFAULT NULL,
  `change_passwd` tinyint(1) NOT NULL DEFAULT '1',
  `never_expire` tinyint(1) NOT NULL DEFAULT '1',
  `bad_passwd_count` smallint(6) DEFAULT '0',
  `last_access` bigint(20) DEFAULT '0',
  `enabled` tinyint(1) NOT NULL DEFAULT '1',
  PRIMARY KEY (`id`),
  UNIQUE KEY `users_username_idx` (`username`)
) ENGINE=MyISAM AUTO_INCREMENT=160 DEFAULT CHARSET=utf8
1 row in set (0.02 sec)

mysql> select count(1) from weisci_jaws_staging2.users;
+----------+
| count(1) |
+----------+
|      117 |
+----------+
1 row in set (0.00 sec)

mysql>

With this table, here are two questions:

• Which columns are nullable ?
• Which columns are not nullable ?

This query will find out for you:

select is_nullable,GROUP_CONCAT(column_name) column_list
from information_schema.columns
where table_schema = 'weisci_jaws_staging2'
and   table_name = 'users'
group by is_nullable;

Check out the result of that query for the table:

mysql> select is_nullable,GROUP_CONCAT(column_name) column_list
    -> from information_schema.columns
    -> where table_schema = 'weisci_jaws_staging2'
    -> and   table_name = 'users'
    -> group by is_nullable;
+-------------+------------------------------------------------------------------------------------------------------------------------------------+
| is_nullable | column_list                                                                                                                        |
+-------------+------------------------------------------------------------------------------------------------------------------------------------+
| NO          | id,never_expire,change_passwd,enabled,username,passwd                                                                              |
| YES         | recovery_key,last_access,bad_passwd_count,updatetime,createtime,last_login,editor,user_type,language,timezone,url,email,name,theme |
+-------------+------------------------------------------------------------------------------------------------------------------------------------+
2 rows in set (0.01 sec)

mysql>

OK, we have two lists. What do we learn from this?

• If you get two lists, no need to inspect the actual table because the table has non-NULL columns by definition.
• If you get one list, then
  • If you get only is_nullable='NO', no need to inspect the actual table because the table has non-NULL columns by definition.
  • If you get only is_nullable='YES', the actual table would be a little brittle. There would be no PRIMARY KEY, you poor, tormented soul !!! NOW, you have to resort to reading every row from the actual table.

If you are looking for just the non-null columns, then this would be your desired query:

select GROUP_CONCAT(column_name) nonnull_columns
from information_schema.columns
where table_schema = 'weisci_jaws_staging2'
and   table_name = 'users'
and   is_nullable = 'NO';

Here is the output of this query:

mysql> select GROUP_CONCAT(column_name) nonnull_columns
    -> from information_schema.columns
    -> where table_schema = 'weisci_jaws_staging2'
    -> and   table_name = 'users'
    -> and   is_nullable = 'NO';
+-------------------------------------------------------+
| nonnull_columns                                       |
+-------------------------------------------------------+
| id,username,passwd,change_passwd,never_expire,enabled |
+-------------------------------------------------------+
1 row in set (0.01 sec)

mysql>

Removing the GROUP_CONCAT, you get this:

mysql> select column_name nonnull_column
    -> from information_schema.columns
    -> where table_schema = 'weisci_jaws_staging2'
    -> and   table_name = 'users'
    -> and   is_nullable = 'NO';
+----------------+
| nonnull_column |
+----------------+
| id             |
| username       |
| passwd         |
| change_passwd  |
| never_expire   |
| enabled        |
+----------------+
6 rows in set (0.01 sec)

mysql>

Give it a Try !!!

NOTE : Please notice that I do not need to read the actual table's data content. That's far more efficient than reading the entire table.

UPDATE 2012-11-15 13:40 EDT

The code from @sensware's answer gives NULL columns. The original question asked for non-NULL columns. I augmented the code to test just my table:

SET group_concat_max_len = 4294967295; -- to overcome default 1KB limitation
SELECT CONCAT(
         'SELECT * FROM ('
       ,  GROUP_CONCAT(
            CONCAT(
              'SELECT ', QUOTE(TABLE_NAME), ' AS `table`,'
            , 'IF('
            ,   'COUNT(`', REPLACE(COLUMN_NAME, '`', '``'), '`),'
            ,   'NULL,'
            ,    QUOTE(COLUMN_NAME)
            , ') AS `column` '
            , 'FROM `',
            REPLACE(TABLE_SCHEMA, '`', '``'), '`.`',
            REPLACE(TABLE_NAME, '`', '``'), '`'
            )
            SEPARATOR ' UNION ALL '
         )
       , ') t WHERE `column` IS NOT NULL'
       )
INTO   @sql
FROM   INFORMATION_SCHEMA.COLUMNS
WHERE  TABLE_SCHEMA = 'weisci_jaws_staging2'
AND    TABLE_NAME = 'users';
SELECT @sql\G
PREPARE stmt FROM @sql;
EXECUTE stmt;
DEALLOCATE PREPARE stmt;

Here is the output:

mysql> SET group_concat_max_len = 4294967295; -- to overcome default 1KB limitation
Query OK, 0 rows affected (0.00 sec)

mysql> SELECT CONCAT(
    ->          'SELECT * FROM ('
    ->        ,  GROUP_CONCAT(
    ->             CONCAT(
    ->               'SELECT ', QUOTE(TABLE_NAME), ' AS `table`,'
    ->             , 'IF('
    ->             ,   'COUNT(`', REPLACE(COLUMN_NAME, '`', '``'), '`),'
    ->             ,   'NULL,'
    ->             ,    QUOTE(COLUMN_NAME)
    ->             , ') AS `column` '
    ->             , 'FROM `',
    ->             REPLACE(TABLE_SCHEMA, '`', '``'), '`.`',
    ->             REPLACE(TABLE_NAME, '`', '``'), '`'
    ->             )
    ->             SEPARATOR ' UNION ALL '
    ->          )
    ->        , ') t WHERE `column` IS NOT NULL'
    ->        )
    -> INTO   @sql
    -> FROM   INFORMATION_SCHEMA.COLUMNS
    -> WHERE  TABLE_SCHEMA = 'weisci_jaws_staging2'
    -> AND    TABLE_NAME = 'users';
Query OK, 1 row affected (0.02 sec)

mysql> SELECT @sql\G
*************************** 1. row ***************************
@sql: SELECT * FROM (SELECT 'users' AS `table`,IF(COUNT(`id`),NULL,'id') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`username`),NULL,'username') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`passwd`),NULL,'passwd') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`user_type`),NULL,'user_type') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`recovery_key`),NULL,'recovery_key') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`name`),NULL,'name') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`email`),NULL,'email') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`url`),NULL,'url') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`timezone`),NULL,'timezone') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`language`),NULL,'language') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`theme`),NULL,'theme') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`editor`),NULL,'editor') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`last_login`),NULL,'last_login') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`createtime`),NULL,'createtime') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`updatetime`),NULL,'updatetime') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`change_passwd`),NULL,'change_passwd') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`never_expire`),NULL,'never_expire') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`bad_passwd_count`),NULL,'bad_passwd_count') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`last_access`),NULL,'last_access') AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`enabled`),NULL,'enabled') AS `column` FROM `weisci_jaws_staging2`.`users`) t WHERE `column` IS NOT NULL
1 row in set (0.00 sec)

mysql> PREPARE stmt FROM @sql;
Query OK, 0 rows affected (0.01 sec)
Statement prepared

mysql> EXECUTE stmt;
+-------+--------+
| table | column |
+-------+--------+
| users | theme  |
+-------+--------+
1 row in set (0.00 sec)

mysql> DEALLOCATE PREPARE stmt;
Query OK, 0 rows affected (0.00 sec)

mysql>

This give NULL columns. The original question asked for non-NULL columns. I'll change the code to generated non-NULL. I'll do that by flipping the order of the IF..COUNT:

SET group_concat_max_len = 4294967295; -- to overcome default 1KB limitation
SELECT CONCAT(
         'SELECT * FROM ('
       ,  GROUP_CONCAT(
            CONCAT(
              'SELECT ', QUOTE(TABLE_NAME), ' AS `table`,'
            , 'IF('
            ,   'COUNT(`', REPLACE(COLUMN_NAME, '`', '``'), '`),'
            ,    QUOTE(COLUMN_NAME)
            ,   ',NULL'
            , ') AS `column` '
            , 'FROM `',
            REPLACE(TABLE_SCHEMA, '`', '``'), '`.`',
            REPLACE(TABLE_NAME, '`', '``'), '`'
            )
            SEPARATOR ' UNION ALL '
         )
       , ') t WHERE `column` IS NOT NULL'
       )
INTO   @sql
FROM   INFORMATION_SCHEMA.COLUMNS
WHERE  TABLE_SCHEMA = 'weisci_jaws_staging2'
AND    TABLE_NAME = 'users';
SELECT @sql\G
PREPARE stmt FROM @sql;
EXECUTE stmt;
DEALLOCATE PREPARE stmt;

Let's run it now...

mysql> SET group_concat_max_len = 4294967295; -- to overcome default 1KB limitation
EXECUTE stmt;
DEALLOCATE PREPARE stmt;
Query OK, 0 rows affected (0.00 sec)

mysql> SELECT CONCAT(
    ->          'SELECT * FROM ('
    ->        ,  GROUP_CONCAT(
    ->             CONCAT(
    ->               'SELECT ', QUOTE(TABLE_NAME), ' AS `table`,'
    ->             , 'IF('
    ->             ,   'COUNT(`', REPLACE(COLUMN_NAME, '`', '``'), '`),'
    ->             ,    QUOTE(COLUMN_NAME)
    ->             ,   ',NULL'
    ->             , ') AS `column` '
    ->             , 'FROM `',
    ->             REPLACE(TABLE_SCHEMA, '`', '``'), '`.`',
    ->             REPLACE(TABLE_NAME, '`', '``'), '`'
    ->             )
    ->             SEPARATOR ' UNION ALL '
    ->          )
    ->        , ') t WHERE `column` IS NOT NULL'
    ->        )
    -> INTO   @sql
    -> FROM   INFORMATION_SCHEMA.COLUMNS
    -> WHERE  TABLE_SCHEMA = 'weisci_jaws_staging2'
    -> AND    TABLE_NAME = 'users';
Query OK, 1 row affected (0.01 sec)

mysql> SELECT @sql\G
*************************** 1. row ***************************
@sql: SELECT * FROM (SELECT 'users' AS `table`,IF(COUNT(`id`),'id',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`username`),'username',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`passwd`),'passwd',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`user_type`),'user_type',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`recovery_key`),'recovery_key',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`name`),'name',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`email`),'email',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`url`),'url',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`timezone`),'timezone',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`language`),'language',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`theme`),'theme',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`editor`),'editor',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`last_login`),'last_login',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`createtime`),'createtime',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`updatetime`),'updatetime',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`change_passwd`),'change_passwd',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`never_expire`),'never_expire',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`bad_passwd_count`),'bad_passwd_count',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`last_access`),'last_access',NULL) AS `column` FROM `weisci_jaws_staging2`.`users` UNION ALL SELECT 'users' AS `table`,IF(COUNT(`enabled`),'enabled',NULL) AS `column` FROM `weisci_jaws_staging2`.`users`) t WHERE `column` IS NOT NULL
1 row in set (0.00 sec)

mysql> PREPARE stmt FROM @sql;
Query OK, 0 rows affected (0.00 sec)
Statement prepared

mysql> EXECUTE stmt;
+-------+------------------+
| table | column           |
+-------+------------------+
| users | id               |
| users | username         |
| users | passwd           |
| users | user_type        |
| users | recovery_key     |
| users | name             |
| users | email            |
| users | url              |
| users | timezone         |
| users | language         |
| users | editor           |
| users | last_login       |
| users | createtime       |
| users | updatetime       |
| users | change_passwd    |
| users | never_expire     |
| users | bad_passwd_count |
| users | last_access      |
| users | enabled          |
+-------+------------------+
19 rows in set (0.01 sec)

mysql> DEALLOCATE PREPARE stmt;
Query OK, 0 rows affected (0.00 sec)

mysql>

OK it works now. There is a problem still present. The query requires reading the entire table. My test table only has 117 rows and 20 columns. What about bigger tables with millions of rows or dozens of columns? I am not going to speculate because I know that the code would be orders of magnitude worse.

That's why I recommend my answer

select GROUP_CONCAT(column_name) nonnull_columns
from information_schema.columns
where table_schema = 'weisci_jaws_staging2'
and   table_name = 'users'
and   is_nullable = 'NO';

or

select column_name nonnull_column
from information_schema.columns
where table_schema = 'weisci_jaws_staging2'
and   table_name = 'users'
and   is_nullable = 'NO';

because the actual data content does not have to be inspected.

The augmented code I made should only be used on a table where all column allow NULL values, which is extremely rare.

You could achieve it by issuing:

SELECT 
  FORMATMESSAGE('SELECT col = ''%s.%s.%s'' FROM %s.%s HAVING COUNT(*) != COUNT(%s)', 
     QUOTENAME(TABLE_SCHEMA),
     QUOTENAME(TABLE_NAME),
     QUOTENAME(COLUMN_NAME),
     QUOTENAME(TABLE_SCHEMA),
     QUOTENAME(TABLE_NAME),
     QUOTENAME(COLUMN_NAME)
  )
FROM INFORMATION_SCHEMA.COLUMNS
WHERE IS_NULLABLE = 'YES';

db<>fiddle demo

It will generate script for checking individual column.

HAVING COUNT(*) != COUNT(col_name) -- it means that column contains at least single NULL

HAVING COUNT(col_name) = 0 AND COUNT(*) != 0 -- it means all values in columns are NULL

This approach could be polished with using STRING_AGG to get single query per table and with dynamic SQL you could avoid the need of copying the query.

EDIT:

Fully baked-solution:

DECLARE @sql NVARCHAR(MAX);

SELECT @sql = STRING_AGG(
  FORMATMESSAGE('SELECT table_schema = ''%s''
                        ,table_name = ''%s''
                        ,table_col_name = ''%s'' 
                        ,row_num = COUNT(*)
                        ,row_num_non_nulls = COUNT(%s)
                        ,row_num_nulls = COUNT(*) - COUNT(%s)
                 FROM %s.%s', 
     QUOTENAME(TABLE_SCHEMA),
     QUOTENAME(TABLE_NAME),
     QUOTENAME(COLUMN_NAME),
     QUOTENAME(COLUMN_NAME),
     QUOTENAME(COLUMN_NAME),
     QUOTENAME(TABLE_SCHEMA),
     QUOTENAME(TABLE_NAME),
     QUOTENAME(COLUMN_NAME)), ' UNION ALL' + CHAR(13)
               ) WITHIN GROUP(ORDER BY TABLE_SCHEMA, TABLE_NAME)

FROM INFORMATION_SCHEMA.COLUMNS
WHERE IS_NULLABLE = 'YES'
  AND TABLE_NAME = ?        -- filter by table name
  AND TABLE_SCHEMA = ?;     -- filter by schema name

SELECT @sql;
EXEC(@sql);

db<>fiddle demo

Output:

+---------------+-----------------+------------------+----------+--------------------+---------------+
| table_schema  |   table_name    | table_col_name   | row_num  | row_num_non_nulls  | row_num_nulls |
+---------------+-----------------+------------------+----------+--------------------+---------------+
| [dbo]         | [StudentScore]  | [Student_Name]   |       7  |                 6  |             1 |
| [dbo]         | [StudentScore]  | [Student_Score]  |       7  |                 5  |             2 |
+---------------+-----------------+------------------+----------+--------------------+---------------+    

Have a look as statistics information, it may be useful for you:

SQL> exec dbms_stats.gather_table_stats('SCOTT','EMP');

PL/SQL procedure successfully completed.

SQL> select num_rows from all_tables where owner='SCOTT' and table_name='EMP';

  NUM_ROWS
----------
        14

SQL> select column_name,nullable,num_distinct,num_nulls from all_tab_columns
  2  where owner='SCOTT' and table_name='EMP' order by column_id;

COLUMN_NAME                    N NUM_DISTINCT  NUM_NULLS
------------------------------ - ------------ ----------
EMPNO                          N           14          0
ENAME                          Y           14          0
JOB                            Y            5          0
MGR                            Y            6          1
HIREDATE                       Y           13          0
SAL                            Y           12          0
COMM                           Y            4         10
DEPTNO                         Y            3          0

8 rows selected.

For example you can check if NUM_NULLS = NUM_ROWS to identify "empty" columns.
Reference: ALL_TAB_COLUMNS, ALL_TABLES.

I do not believe there is a simple "SELECT * FROM [TABLE]" query that would exclude a column based on all of the values contained in the column in your result set. The select clause is defining what data to bring back, the from clause tells it ..well where from, and a where clause provides filtering criteria at a row-level.

The query you are talking about can almost certainly be written but it would not be a simple select * from [table].

Not all databases support boolean types. You can use case as:

SELECT name AS UserName, age AS UserAge,
       (CASE WHEN birthday IS NOT NULL THEN 'true' ELSE 'false' END) AS HasEnteredBirthday
FROM users;

Often, the integer "1" is used for true and "0" for false.