You need to add a callback to the URL to make it a JSONP request because you cannot do cross domain JSON requests.
So to fix your code, it's as easy as adding '?callback=?' to the end of your URL.
$.getJSON("http://api.twitter.com/1/statuses/user_timeline/jrock2004.json?callback=?", function(data) {
$.each(data, function(){
$('<div></div>')
.hide()
.append('<span>' + this.text + '</span>')
.appendTo('#tweets')
.fadeIn();
});
});