Public launch September 17 ahead of iPhone 6 debut.
Game Center Games Starting to Appear in App Store
A forum thread on TouchArcade is maintaining a list of current and expected Game Center enabled games. Game Center offers a centralized achievement and leaderboard system for the iOS platform. In addition, Game Center provides matchmaking capabilities for multi-player games.
Here are some notable games that have been updated to support leaderboards and achievements: Ms. Pac Man, Real Racing, Flight Control. Pangea Software appears to be the first to include online multi-player support in Enigmo, Cro Mag Rally, and Nanosaur 2. For a full list, see TouchArcade.
Update: Apple now has a featured Game Center section on the App Store