Well, because of the slow data transfer speed, there aren't many online games for PDAs out there. The ones that are out there are mostly chess games, dart games, or casino games.
www.banywhere.com has a chess game you can download. http://www.dorcino.com/dorcino2/palm7/ has a few greyscale casino games. Some other online casino or lotto sites have pqas for Palm users to play online. Omnisky was a good wireless provider if you are a Pocket PC user. But they got bought and have not updated their service to support new PDA models. ID Games just recently announced a multi-player mobile chess game and poker game that you can play with your Pocket PC for a download fee and 1 year subscription.