Maybe the next version of Apple's iPhone will have games, but for now only a few have been ported to iPhone by developers. iChess lets you play the classic game against an AI opponent. One word of warning: if you set the level of the AI too high, you're going to be waiting for a long time to make your next move.
iPhone link:
http://ec2-72-44-51-230.z-1.compute-1.amazonaws.com/ichess.html