I don't know if I'd call this a game, but it is good for community building/helping the students get to know each other.
I read
A Bad Case of Stripes by David Shannon (love it!) and then we talk about being unique and accepting other people's uniqueness. I give each student an index card and they write one special thing about themselves on there (favorite color, favorite sport, a cool fact, etc.). Then, we sit in a circle with a ball of yarn...I share my fact, then throw the yarn to the next volunteer. They do the same (holding on to their own piece of yarn). It goes on and on until everyone has shared and is holding a part of the yarn. We talk about the "web of friendship" that we've created; as a class, we have to respect and look out for each other.
Kind of cheesy and it may not be quite what you're looking for, but I love it. We did it the 2nd day of school this year (2 weeks ago), and my students still ask if we can do it again!
I've also gotten some ideas from this site:
http://www2.scholastic.com/browse/co.../tout_txtl////
Actually, the friendship web may have come from there. Hope some of this helps!