JavaScript check if variable exists (is defined/initialized)

You want the typeof operator. Specifically:

if (typeof variable !== 'undefined') {    // the variable is defined}

The typeof operator will check if the variable is really undefined.

if (typeof variable === 'undefined') {    // variable is undefined}

The typeof operator, unlike the other operators, doesn't throw a ReferenceError exception when used with an undeclared variable.

However, do note that typeof null will return "object". We have to be careful to avoid the mistake of initializing a variable to null. To be safe, this is what we could use instead:

if (typeof variable === 'undefined' || variable === null) {    // variable is undefined or null}

For more info on using strict comparison === instead of simple equality ==, see:
Which equals operator (== vs ===) should be used in JavaScript comparisons?

In many cases, using:

if (elem) { // or !elem

will do the job for you!... this will check these below cases:

1. undefined: if the value is not defined and it's undefined
2. null: if it's null, for example, if a DOM element not exists...
3. empty string: ''
4. 0: number zero
5. NaN: not a number
6. false

So it will cover off kind of all cases, but there are always weird cases which we'd like to cover as well, for example, a string with spaces, like this ' ' one, this will be defined in javascript as it has spaces inside string... for example in this case you add one more check using trim(), like:

if(elem) {if(typeof elem === 'string' && elem.trim()) {///

Also, these checks are for values only, as objects and arrays work differently in Javascript, empty array [] and empty object {} are always true.

I create the image below to show a quick brief of the answer: