I wish to do a turn based multiplayer game like Words with friends on the iphone. I would like to know the approach for the implementation to allow the user to continue games that are currently still active even after a couple of days. Is this even possible using Game Center?
All that you need to do is store the game state somewhere persistent where all the players can get at it. For example in a database accessed via a web server. That server could also process each players turns on the game if you want it to (this helps prevent cheating). You can then easily control how long it stores the game state for. For example it would appear words with friends simply allows a maximum of 20 in progress games per player, and the game state is probably no more than a few hundred bytes per game so the storage requirements on the server would be quite small.
I'm not certain about Game Center, but a quick look suggests that as long as your game can get at the User ID of the player that's all you'd need to track the game in your database.