I saw a review of PlayMyGame.com in TechCrunch this morning - this is a German site that has tools that let a user customize simple games with their own picture. As Michael Arrington at TechCrunch noted: the tools to create a customized game are very easy to use and you can have your own game in a couple of minutes. Once the games are complete they can be embedded into a website - as I have done with my own game, below:

I also wrote about creating more sophisticated games using this platform (down the line) here. I imagine it would also be possible for a group to create a game(s) although the PlayMyGame platform is not set up for that yet.