Many phones include simple games for the user to pass the time when waiting, travelling, etc. The games referred to here are ones built into the phone, that do not require a connection and airtime to play. (There are games available over the Wireless Internet that do require a connection and thus airtime.)
Many phones also include the ability to download new games wirelessly. There are several different technologies for downloadable games, including Java, BREW, Mophun, and WGE. The technologies are incompatible, although some phones support more than one technology.