If you are explicitly setting the value to NULL in your insert, but want MySQL to replace the NULL with 0, one way to do that is to define the column to allow NULL in the CREATE TABLE statement, and then replace the NULL with a TRIGGER.

Something like this:

CREATE TABLE `listings` (
  `ListingID` int(11) NOT NULL,
  `BathsFull` int(6) NULL DEFAULT 0,
  PRIMARY KEY (`ListingID`)
) ENGINE=InnoDB DEFAULT CHARSET=latin1;

delimiter $$

create trigger tr_b_ins_listings before insert on listings for each row
begin
  set new.BathsFull = coalesce(new.BathsFull,0);
end $$

delimiter ;

Try it for yourself in this SQL Fiddle

In MySQL, each column type has an "implicit default" value.

For string types [the implicit] default value is the empty string.

If a NOT NULL column is added to a table, and no explicit DEFAULT is specified, the implicit default value is used to populate the new column data¹. Similar rules apply when the DEFAULT value is specified.

As such, the original DDL produces the same results as:

-- After this, data will be the same, but schema has an EXPLICIT DEFAULT
ALTER TABLE t ADD c varchar(10) NOT NULL DEFAULT ''
-- Now we're back to the IMPLICIT DEFAULT (MySQL stores NULL internally)
ALTER TABLE t ALTER c DROP DEFAULT

The "strict" mode settings affects DML statements relying on default values, but do not affect the implicit default usage when the column is added.

For data entry into a NOT NULL column that has no explicit DEFAULT clause, if an INSERT or REPLACE statement includes no value for the column [and if] strict SQL mode is enabled, an error occurs ..

Here is an sqlfiddle "proof" that strict mode does not apply to the ALTER TABLE .. ADD statement.

¹ This is a MySQL feature. Other engines, like SQL Server, require an explicit DEFAULT (or NULL column) constraint for such schema changes.

That's perfectly acceptable, it basically states:

You have to provide a value for this, but I have no clue what that would be.

If you define a default value, you claim that this is a sensible value for any row that doesn't supply a value - which is not really feasible for most attributes.

Think about a column named first_name - you want to make sure a value is supplied but there is no way you can come up with a sensible default value for that. Or a column named salary in an employee table.

I couldn't find this behavior described in the official MySQL documentation

A few minutes of looking in the MySQL docs found this:

Column values can be given in several ways:

If you are not running in strict SQL mode, any column
not explicitly given a value is set to its default
(explicit or implicit) value. For example, if you specify a
column list that does not name all the columns in the
table, unnamed columns are set to their default values.
Default value assignment is described in Section 11.6,
“Data Type Default Values”. See also Section 1.8.3.3,
“Constraints on Invalid Data”.

If you want an INSERT statement to generate an error unless
you explicitly specify values for all columns that do not
have a default value, you should use strict mode. See
Section 5.1.7, “Server SQL Modes”.

Referring to the manual,

For data entry for a NOT NULL column that has no explicit DEFAULT clause, if an INSERT or REPLACE statement includes no value for the column, or an UPDATE statement sets the column to NULL, MySQL handles the column according to the SQL mode in effect at the time:

• If strict SQL mode is not enabled, MySQL sets the column to the implicit default value for the column data type.
• If strict mode is enabled, an error occurs for transactional tables and the statement is rolled back. For nontransactional tables, an
  error occurs, but if this happens for the second or subsequent row of a multiple-row statement, the preceding rows will have been inserted.

So your question now may be, what are the implicit default values for the various column data types? Here you go:

Implicit defaults are defined as follows:

• For numeric types, the default is 0, with the exception that for integer or floating-point types declared with the AUTO_INCREMENT
  attribute, the default is the next value in the sequence.
• For date and time types other than TIMESTAMP, the default is the appropriate “zero” value for the type. For the first TIMESTAMP column in a table, the default value is the current date and time. See Section 10.3, “Date and Time Types”.
• For string types other than ENUM, the default value is the empty string. For ENUM, the default is the first enumeration value.

The answer is to use the following (slightly odd) syntax:

ALTER TABLE items ALTER ordering DROP DEFAULT;

Use the DEFAULT keyword instead:

INSERT INTO users (TimeZoneId) VALUES (DEFAULT);

To insert the default value, you have to not specify any value for the column, not even NULL, because NULL is a specific value.

Are you using a framework where objects are automatically converted into SQL statements for saving? If the value of the property in your PHP class is not set and the column is nullable then it will insert null instead of 0.

Consider:

class Foo{
    protected $propertyName;
}

That is equivalent in PHP to

class Foo{
    protected $propertyName = null;
}

If the TINYINT(4) column for propertyName is nullable when it builds the query to save the data it will save as null in the database. If you are using a design pattern like this you need set the default value in the PHP class itself. Something like

class Foo{
    protected $propertyName = 0;
}

Note, if the column is not null-able then saving the object would throw an error in this scenario. If you wanted to get fancy, you can fetch the default values for a column using

DESC tableName;

That will return information about the table, there will be a column NULL which will be YES or NO (describing if the column is null-able). And a column Default which will be the default value (or NULL if there is none). You could then populate null fields in your class based on the default values from the database. You would want to be careful here as there are likely some columns that should be NULL. Ideally, you would make any fields that can't accept null non-nullable and then key your logic for handling defaults only fire when the Null column is NO.

First of all: Every column has a default value. In many cases this default value is NULL, but if declared NOT NULL it must obviously be something else.

With the TIMESTAMP data type, the default value is CURRENT_TIMESTAMP(), but of course this can be overwritten:

createDate TIMESTAMP(3) NOT NULL DEFAULT '0000-01-01 00:00:00'

will e.g. set a default value of 0.0 A.D.