Ways to clear an existing array A:

Method 1

(this was my original answer to the question)

A = [];

This code will set the variable A to a new empty array. This is perfect if you don't have references to the original array A anywhere else because this actually creates a brand new (empty) array. You should be careful with this method because if you have referenced this array from another variable or property, the original array will remain unchanged. Only use this if you only reference the array by its original variable A.

This is also the fastest solution.

This code sample shows the issue you can encounter when using this method:

var arr1 = ['a','b','c','d','e','f'];
var arr2 = arr1;  // Reference arr1 by another variable 
arr1 = [];
console.log(arr2); // Output ['a','b','c','d','e','f']

Method 2 (as suggested by Matthew Crumley)

A.length = 0

This will clear the existing array by setting its length to 0. It also works when using "strict mode" in ECMAScript 5 because the length property of an array is a read/write property.

Method 3 (as suggested by Anthony)

A.splice(0,A.length)

Using .splice() will work perfectly, but since the .splice() function will return an array with all the removed items, it will actually return a copy of the original array. Benchmarks suggest that this has no effect on performance whatsoever.

Method 4 (as suggested by tanguy_k)

while(A.length > 0) {
    A.pop();
}

This solution is not very succinct, and it is also the slowest solution, contrary to earlier benchmarks referenced in the original answer.

Performance

Of all the methods of clearing an existing array, methods 2 and 3 are very similar in performance and are a lot faster than method 4. See this benchmark.

As pointed out by Diadistis in their answer below, the original benchmarks that were used to determine the performance of the four methods described above were flawed. The original benchmark reused the cleared array so the second iteration was clearing an array that was already empty.

The following benchmark fixes this flaw: http://jsben.ch/#/hyj65. It clearly shows that methods #2 (length property) and #3 (splice) are the fastest (not counting method #1 which doesn't change the original array).

This has been a hot topic and the cause of a lot of controversy. There are actually many correct answers and because this answer has been marked as the accepted answer for a very long time, I will include all of the methods here.

You want to do the check for undefined first. If you do it the other way round, it will generate an error if the array is undefined.

if (array === undefined || array.length == 0) {
    // array does not exist or is empty
}

Update

This answer is getting a fair amount of attention, so I'd like to point out that my original answer, more than anything else, addressed the wrong order of the conditions being evaluated in the question. In this sense, it fails to address several scenarios, such as null values, other types of objects with a length property, etc. It is also not very idiomatic JavaScript.

The foolproof approach
Taking some inspiration from the comments, below is what I currently consider to be the foolproof way to check whether an array is empty or does not exist. It also takes into account that the variable might not refer to an array, but to some other type of object with a length property.

if (!Array.isArray(array) || !array.length) {
  // array does not exist, is not an array, or is empty
  // ⇒ do not attempt to process array
}

To break it down:

1. Array.isArray(), unsurprisingly, checks whether its argument is an array. This weeds out values like null, undefined and anything else that is not an array.
   Note that this will also eliminate array-like objects, such as the arguments object and DOM NodeList objects. Depending on your situation, this might not be the behavior you're after.

2. The array.length condition checks whether the variable's length property evaluates to a truthy value. Because the previous condition already established that we are indeed dealing with an array, more strict comparisons like array.length != 0 or array.length !== 0 are not required here.

The pragmatic approach
In a lot of cases, the above might seem like overkill. Maybe you're using a higher order language like TypeScript that does most of the type-checking for you at compile-time, or you really don't care whether the object is actually an array, or just array-like.

In those cases, I tend to go for the following, more idiomatic JavaScript:

if (!array || !array.length) {
    // array or array.length are falsy
    // ⇒ do not attempt to process array
}

Or, more frequently, its inverse:

if (array && array.length) {
    // array and array.length are truthy
    // ⇒ probably OK to process array
}

With the introduction of the optional chaining operator (Elvis operator) in ECMAScript 2020, this can be shortened even further:

if (!array?.length) {
    // array or array.length are falsy
    // ⇒ do not attempt to process array
}

Or the opposite:

if (array?.length) {
    // array and array.length are truthy
    // ⇒ probably OK to process array
}