Irving Chernev ranked Bogolyubov-Alekhine, Hastings 1922 as the greatest game ever played and Pillsbury-Tarrasch, Hastings 1895 as the second greatest. Of course this was several decades ago, but both games are still pretty awesome! Here's some lists with lots of other great (and maybe a few not-so-great) suggestions:
http://www.chessgames.com/perl/chesscollection?cid=1003368
http://www.chessgames.com/perl/chesscollection?cid=1001601
http://www.dailymail.co.uk/home/moslive/article-1340520/10-greatest-chess-games-From-Kasporov-vs-Bobby-Fischers-victory.html
This is a thread to see what are the top ten bst chess games ever
I will give 2 to start off.