Balanced parentheses
This is almost all style suggestions; the code itself looks great.

Personally, I prefer the brace-on-same-line style for everything in JS, and I prefer proper blocks instead of inlining expressions. But those are just preferences. I've also skipped the bitwise trick, added some strict comparisons instead of !stack.length etc., moved the i++ over to its "usual" place, and lengthened a few variable names, just for clarity.

Again: This is all basically pointless, but I just like spelling things out.

The only real difference is that rather than push the opening brace onto the stack, I push the position of the expected closing brace. It just makes the conditional a bit cleaner later on.

function parenthesesAreBalanced(string) {
  var parentheses = "[]{}()",
    stack = [],
    i, character, bracePosition;

  for(i = 0; character = string[i]; i++) {
    bracePosition = parentheses.indexOf(character);

    if(bracePosition === -1) {
      continue;
    }

    if(bracePosition % 2 === 0) {
      stack.push(bracePosition + 1); // push next expected brace position
    } else {
      if(stack.length === 0 || stack.pop() !== bracePosition) {
        return false;
      }
    }
  }

  return stack.length === 0;
}




Update: Actually, you can skip one stack.length check in the inner conditional; stack.pop() will just return undefined if the stack's empty, so this is enough:

if(stack.pop() !== bracePosition) {
  return false;
}