Try the codblops 2 forums.

Perhaps you ran into a server admin who is a religious zealot... (your screen name).
Are you able to play on other servers?
Some games let the admin write a message for why you were kicked. On other servers even if there is room there might be player slot reservation. A paying member(of their group) will always get in, kicking you (the public) off.

There is, most likely, a forum relating to game in your question. What games that is, I don't know because you don't say. If you have a game-specific question, ask it in their forum. This is for conversations regarding Steam as a whole, not specific games and troubleshooting.

Happens to me and it seems related to friendly fire in hardcore game mode. Seems as if it kicks you when kill team mates 2 or 3 times, bit daft as a lot of the time teamates run into your line of fire. Sound as though it could be that?