How do I split a string into an array of characters?

You can split on an empty string:

var chars = "overpopulation".split('');

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If you just want to access a string in an array-like fashion, you can do that without split:

var s = "overpopulation";
for (var i = 0; i < s.length; i++) {
    console.log(s.charAt(i));
}

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You can also access each character with its index using normal array syntax. Note, however, that strings are immutable, which means you can't set the value of a character using this method, and that it isn't supported by IE7 (if that still matters to you).

var s = "overpopulation";

console.log(s[3]); // logs 'r'

Old question but I should warn:

Do NOT use .split('')

You'll get weird results with non-BMP (non-Basic-Multilingual-Plane) character sets.

Reason is that methods like .split() and .charCodeAt() only respect the characters with a code point below 65536; bec. higher code points are represented by a pair of (lower valued) "surrogate" pseudo-characters.

'𝟙𝟚𝟛'.length     // —> 6
'𝟙𝟚𝟛'.split('')  // —> ["�", "�", "�", "�", "�", "�"]

'😎'.length      // —> 2
'😎'.split('')   // —> ["�", "�"]

Use ES2015 (ES6) features where possible:

Using the spread operator:

let arr = [...str];

Or Array.from

let arr = Array.from(str);

Or split with the new u RegExp flag:

let arr = str.split(/(?!$)/u);

Examples:

[...'𝟙𝟚𝟛']        // —> ["𝟙", "𝟚", "𝟛"]
[...'😎😜🙃']     // —> ["😎", "😜", "🙃"]

For ES5, options are limited:

I came up with this function that internally uses MDN example to get the correct code point of each character.

function stringToArray() {
  var i = 0,
    arr = [],
    codePoint;
  while (!isNaN(codePoint = knownCharCodeAt(str, i))) {
    arr.push(String.fromCodePoint(codePoint));
    i++;
  }
  return arr;
}

This requires knownCharCodeAt() function and for some browsers; a String.fromCodePoint() polyfill.

if (!String.fromCodePoint) {
// ES6 Unicode Shims 0.1 , © 2012 Steven Levithan , MIT License
    String.fromCodePoint = function fromCodePoint () {
        var chars = [], point, offset, units, i;
        for (i = 0; i < arguments.length; ++i) {
            point = arguments[i];
            offset = point - 0x10000;
            units = point > 0xFFFF ? [0xD800 + (offset >> 10), 0xDC00 + (offset & 0x3FF)] : [point];
            chars.push(String.fromCharCode.apply(null, units));
        }
        return chars.join("");
    }
}

Examples:

stringToArray('𝟙𝟚𝟛')     // —> ["𝟙", "𝟚", "𝟛"]
stringToArray('😎😜🙃')  // —> ["😎", "😜", "🙃"]

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Note: str[index] (ES5) and str.charAt(index) will also return weird results with non-BMP charsets. e.g. '😎'.charAt(0) returns "�".

UPDATE: Read this nice article about JS and unicode.