Functional-style answers for You Can('t) Javascript Under Pressure, v1.0

level1.js

function doubleInteger(i) {
  return i * 2;
}

level2.js

function isNumberEven(i) {
  return !(i % 2);
}

level3.js

function getFileExtension(i) {
  var s = i.split('.');
  return s.length > 1 ? s.pop() : false;
}

level4.js

function longestString(i) {
  return i.sort(function(a, b) {
    return typeof a == 'string' && typeof b == 'string' ? a.length - b.length : -1;
  }).pop();
}

level5.js

function arraySum(i) {
  return i.reduce(function(memo, a) {
    return memo + (
      typeof a === 'number' ? a : (
        Array.isArray(a) ? arraySum(a) : 0
      )
    );
  }, 0);
}

Alternate versions and performance tests for Level 4: http://jsperf.com/ycjup-level4