You can do so:

var N = 10; 
Array.apply(null, {length: N}).map(Number.call, Number)

result: [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

or with random values:

Array.apply(null, {length: N}).map(Function.call, Math.random)

result: [0.7082694901619107, 0.9572225909214467, 0.8586748542729765, 0.8653848143294454, 0.008339877473190427, 0.9911756622605026, 0.8133423360995948, 0.8377588465809822, 0.5577575915958732, 0.16363654541783035]

Explanation

First, note that Number.call(undefined, N) is equivalent to Number(N), which just returns N. We'll use that fact later.

Array.apply(null, [undefined, undefined, undefined]) is equivalent to Array(undefined, undefined, undefined), which produces a three-element array and assigns undefined to each element.

How can you generalize that to N elements? Consider how Array() works, which goes something like this:

function Array() {
    if ( arguments.length == 1 &&
         'number' === typeof arguments[0] &&
         arguments[0] >= 0 && arguments &&
         arguments[0] < 1 << 32 ) {
        return [ … ];  // array of length arguments[0], generated by native code
    }
    var a = [];
    for (var i = 0; i < arguments.length; i++) {
        a.push(arguments[i]);
    }
    return a;
}

Since ECMAScript 5, Function.prototype.apply(thisArg, argsArray) also accepts a duck-typed array-like object as its second parameter. If we invoke Array.apply(null, { length: N }), then it will execute

function Array() {
    var a = [];
    for (var i = 0; i < /* arguments.length = */ N; i++) {
        a.push(/* arguments[i] = */ undefined);
    }
    return a;
}

Now we have an N-element array, with each element set to undefined. When we call .map(callback, thisArg) on it, each element will be set to the result of callback.call(thisArg, element, index, array). Therefore, [undefined, undefined, …, undefined].map(Number.call, Number) would map each element to (Number.call).call(Number, undefined, index, array), which is the same as Number.call(undefined, index, array), which, as we observed earlier, evaluates to index. That completes the array whose elements are the same as their index.

Why go through the trouble of Array.apply(null, {length: N}) instead of just Array(N)? After all, both expressions would result an an N-element array of undefined elements. The difference is that in the former expression, each element is explicitly set to undefined, whereas in the latter, each element was never set. According to the documentation of .map():

callback is invoked only for indexes of the array which have assigned values; it is not invoked for indexes which have been deleted or which have never been assigned values.

Therefore, Array(N) is insufficient; Array(N).map(Number.call, Number) would result in an uninitialized array of length N.

Compatibility

Since this technique relies on behaviour of Function.prototype.apply() specified in ECMAScript 5, it will not work in pre-ECMAScript 5 browsers such as Chrome 14 and Internet Explorer 9.

For numbers you can use ES6 Array.from(), which works in everything these days except IE:

Shorter version:

Array.from({length: 20}, (x, i) => i);

Longer version:

Array.from(new Array(20), (x, i) => i);​​​​​​

which creates an array from 0 to 19 inclusive. This can be further shortened to one of these forms:

Array.from(Array(20).keys());
// or
[...Array(20).keys()];

Lower and upper bounds can be specified too, for example:

Array.from(new Array(20), (x, i) => i + *lowerBound*);

An article describing this in more detail: http://www.2ality.com/2014/05/es6-array-methods.html