If you have an iPhone 4 / 3GS, You can install Game center by updating iOS 4 to 4.1.

Its more like Xbox Live -- you can invite friends to games, rack up achievements and get paired with strangers of similar skill in multiplayer … You can even hook up & pass your leisure gossiping as it has a social layer too – at least that was the original concept. But actually aside from adding friends and altering a status message, there isn't anything to do in Game Center. To speak the truth -- A button for "Find Game Center Games" boots the player out Apple's Game Center web page, which is basically an advertisement with no resources. So after adding friends and sharing a status message, you may wonder (like me!) what to do next?? There's no way to figure out which game will support Game Center from within the app (AFAIK -- Ms. Pac-Man is the first game to support Game Center).

Really Apple needs to go a long way to be a competitor of Microsoft in the ‘Gaming world’.