Another method is to memoize the recursive function by extending it with a cache defined inside a closure. This combines the simplicity of the recursive method with the advantages of only calculating each value once.

cachingFibonacci.js

var fibClosure = (function() {
  var cache = [0,1,1];
  return function(n) {
    if (cache[n] === undefined) {
      cache[n] = fibClosure(n - 1) + fibClosure(n - 2);
    }
    return cache[n];
  };
}());