This question has two interpretations:

Check if the variable has a value
Check if the variable has a truthy value

The following answers both.

In JavaScript, a value could be nullish or not nullish, and a value could be falsy or truthy.
Nullish values are a proper subset of falsy values:

 ╭─ nullish ──────╮ ╭─ not nullish ─────────────────────────────────╮
┌───────────┬──────┬───────┬───┬────┬─────┬──────┬───┬─────────┬─────┐
│ undefined │ null │ false │ 0 │ "" │ ... │ true │ 1 │ "hello" │ ... │
└───────────┴──────┴───────┴───┴────┴─────┴──────┴───┴─────────┴─────┘
 ╰─ falsy ───────────────────────────────╯ ╰─ truthy ───────────────╯

Check if value is nullish (undefined or null)

Use one of the following depending on your coding style:

if (value == null)                         { /* value is nullish */ }
if (value === undefined || value === null) { /* value is nullish */ }
if (value == undefined)                    { /* value is nullish */ }
if ((value ?? null) === null)              { /* value is nullish */ }

Notes:

• The == operator works because it has a special case for null vs undefined comparison
• The === operator is more readable (opinion based), eqeqeq friendly and allows checking for undefined and null separately
• The first and third examples work identically, however the third one is rarely seen in production code
• The fourth example uses nullish coalescing operator to change nullish values to null for straight forward comparison

Check if value is not nullish

if (value != null)                         { /* value is not nullish, although it could be falsy */ }
if (value !== undefined && value !== null) { /* value is not nullish, although it could be falsy */ }
if (value != undefined)                    { /* value is not nullish, although it could be falsy */ }
if ((value ?? null) !== null)              { /* value is not nullish, although it could be falsy */ }

Check if value is falsy

Use the ! operator:

if (!value) { /* value is falsy */ }

Check if value is truthy

if (value) { /* value is truthy */ }

Data validation

The nullish, falsy and truthy checks cannot be used for data validation on their own. For example, 0 (falsy) is valid age of a person and -1 (truthy) is not. Additional logic needs to be added on case-by-case basis. Some examples:

/*
 * check if value is greater than/equal to 0
 * note that we cannot use truthy check here because 0 must be allowed
 */
[null, -1, 0, 1].forEach(num => {
  if (num != null && num >= 0) {
    console.log("%o is not nullish and greater than/equal to 0", num);
  } else {
    console.log("%o is bad", num);
  }
});

/*
 * check if value is not empty-or-whitespace string
 */
[null, "", " ", "hello"].forEach(str => {
  if (str && /\S/.test(str)) {
    console.log("%o is truthy and has non-whitespace characters", str);
  } else {
    console.log("%o is bad", str);
  }
});

/*
 * check if value is not an empty array
 * check for truthy before checking the length property
 */
[null, [], [1]].forEach(arr => {
  if (arr && arr.length) {
    console.log("%o is truthy and has one or more items", arr);
  } else {
    console.log("%o is bad", arr);
  }
});

/*
 * check if value is not an empty array
 * using optional chaining operator to make sure that the value is not nullish
 */
[null, [], [1]].forEach(arr => {
  if (arr?.length) {
    console.log("%o is not nullish and has one or more items", arr);
  } else {
    console.log("%o is bad", arr);
  }
});

Ignoring whitespace strings, you could use this to check for null, empty and undefined:

var obj = {};
(!!obj.str) // Returns false

obj.str = "";
(!!obj.str) // Returns false

obj.str = null;
(!!obj.str) // Returns false

It is concise and it works for undefined properties, although it's not the most readable.

This is a bigger question than you think. Variables can empty in a lot of ways. Kinda depends on what you need to know.

// quick and dirty will be true for '', null, undefined, 0, NaN and false.
if (!x) 

// test for null OR undefined
if (x == null)  

// test for undefined OR null 
if (x == undefined) 

// test for undefined
if (x === undefined) 
// or safer test for undefined since the variable undefined can be set causing tests against it to fail.
if (typeof x == 'undefined') 

// test for empty string
if (x === '') 

// if you know its an array
if (x.length == 0)  
// or
if (!x.length)

// BONUS test for empty object
var empty = true, fld;
for (fld in x) {
  empty = false;
  break;
}