Edit in JSFiddle

//////////////////////////////////////
// Max in Array
//////////////////////////////////////
function max(arr) {
  var m;
  for(var i=0; i < arr.length; i++)
  {
      if(i==0) {
          m = arr[i];
          continue;
      }
      
      if(arr[i] > m)
      {
          m = arr[i];
      }
  } 
  return m;
}

var myArray = [-1,-2,-3,100,5];
log("Max in Array");
log(max(myArray));

log("Max in Array with library");
log(Math.max.apply(null,myArray));

//////////////////////////////////////
// LINKED LIST
//////////////////////////////////////
function LinkedList() {}
LinkedList.prototype = {
  length: 0,
  head: null,
  tail: null
};
LinkedList.Node = function(data) {
  this.prev = null; 
  this.next = null;
  this.data = data;
};
LinkedList.prototype.append = function(node) {
  if (this.head === null) {
    node.prev = null;
    node.next = null;
    this.head = node;
    this.tail = node;
  } else {
    this.tail.next = node;
    this.prev = this.tail;
    this.tail = node;      
  }
  this.length++;
};

var myList = new LinkedList();
myList.append(new LinkedList.Node("a"));
myList.append(new LinkedList.Node("b"));
myList.append(new LinkedList.Node("c"));

log("Linked list");
var node = myList.head;
for(var i=0; i<myList.length; i++)
{
    log(node.data);
    node = node.next;
}

log("Linked list reveresed");
reverseLinkedList(myList);
var node1 = myList.head;
for(var i=0; i<myList.length; i++)
{
    log(node1.data);
    node1 = node1.next;
}

function reverseLinkedList (linkedList)
{
     var temp = null;
     var current = linkedList.head;
 
     // swap next and prev for all nodes of doubly linked list 
     while (current != null)
     {
       current.prev = current.next;
       current.next = temp;
       temp = current;
       current = current.prev;
     }
     linkedList.head = temp;
}

//////////////////////////////////////
// fibonacci - Fn = Fn-1 + Fn-2
//F0    F1    F2    F3    F4    F5    F6    F7    F8    F9    F10    F11    
// 0     1     1     2     3     5     8    13    21    34     55     89 
//////////////////////////////////////  
function fibonacci(n) {
    if (n <= 1) return n;
    return fibonacci(n - 2) + fibonacci(n - 1);
}

fibonacciCache = (function () {
    var cache = { 0:0, 1:1 };

    return function (n) {
        var cached = cache[n];
        if (typeof cached !== 'undefined') return cached;

        return (cache[n] = fibonacciCache(n - 2) + fibonacciCache(n - 1));
    };
}());

log("Fibonacci of 11");
log(fibonacci(11));
log("fibonacci of 25 with cache");
log(fibonacciCache(25));

//////////////////////////////////////
// Pub sub
//////////////////////////////////////
/* jQuery Tiny Pub/Sub - v0.7 - 10/27/2011
 * http://benalman.com/
 * Copyright (c) 2011 "Cowboy" Ben Alman; Licensed MIT, GPL */

(function($) {

  var o = $({});

  $.subscribe = function() {
    o.on.apply(o, arguments);
  };

  $.unsubscribe = function() {
    o.off.apply(o, arguments);
  };

  $.publish = function() {
    o.trigger.apply(o, arguments);
  };

}(jQuery));

log("Pub / sub");
$.subscribe("/some/topic", function(e, a, b, c) {  // subscrbe
    log(a + b + c);
});
$.subscribe("/some/topic", function(e, a, b, c) {  // subscrbe
    log("Subscriber 2: " + a + b + c);
});
$.publish("/some/topic", [ "a", "b", "c" ]);       // publish
$.unsubscribe("/some/topic"); // Unsubscribe all handlers for this topic


//////////////////////////////////////
// Helpers
//////////////////////////////////////
function log(m) {
  $("#info").append(m + "<br/>");
}

JavaScript Samples
<div id="info"></div>