DO I have a BIG hurdle wanting to run a game on Game Center without using my own server? Apparently this cuts out 3G devices which cold be massive sales loss! Not only that how do you run a game on Android. Is there some kind of Game Center that Android has for publishers?
Game Center and Open Feint servers will handle your achievements, highscores and multiplayer matching, plus Open Feint also has other features to enable Freemium features, but if your entire game is based on users being fully connected everytime they play (e.g. WeRule, City Story etc), then you need to have servers to manage the game data, and if you're very successful you'll need to be able to scale that up to deal with the increasing number of players. Game Center isn't designed to do that part, it's really just for the scores, awards and player matching right now.
If you don't need a persistent connection (i.e. You need occasional updates), then check this out: http://code.google.com/appengine/ If you absolutely need persistent connections, check out a VPS solution for inexpensive hosting. Here's the first option that came up on Google: http://myhosting.com/virtual-server-hosting/