Displaying random quotes from an array
I think your code looks pretty good already. It follows conventions and your indentation and variable names are precise. There's not much to review.

But if you're targeting modern browsers (IE9+) I would suggest a different approach using map and would separate the random logic into a function. I'd also declare the element up top so I know at first glance that the code is working with the DOM. It may seem like more code at first but it's good for code reuse, plus I think it reads better; the intent is more clear:

(function() {
  "use strict";

  var el = document.getElementById("quotes");

  var quotes = [
    ["Stay Hungry. Stay Foolish.", "Steve Jobs"],
    ["Good Artists Copy, Great Artists Steal.", "Pablo Picasso"],
    ["Argue with idiots, and you become an idiot.", "Paul Graham"],
    ["Be yourself; everyone else is already taken.", "Oscar Wilde"],
    ["Simplicity is the ultimate sophistication.", "Leonardo Da Vinci"]
  ];

  function rand(xs) {
    return xs.slice(0).sort(function(){
      return .5 - Math.random();
    });
  }

  function quote(q) {
    return "&lt;p&gt;&amp;ldquo;"+ q[0] +"&amp;rdquo; &amp;mdash; &lt;em&gt;"+ q[1] +"&lt;/em&gt;&lt;/p&gt;";
  }

  el.innerHTML = rand(quotes).map(quote).join('');

}());