Like Agamer said, a server meant for hosting games will generally need a bit more power than one used just for serving web pages. Having said that, any reasonably configured dedicated server should be capable of handling a decent load and should allow you to run your own game server, assuming you have the proper libraries and support files installed. Even a shared server that is not overpopulated would probably be able to support a moderate gaming load, but your host will almost certainly disallow that sort of activity on a shared box.
SpaceAce
SpaceAce