How do I receive bitcoins for a game server?
I've fiddled a bit with the plain vanilla reference bitcoin client, with the JSON-RPC server enabled, and it's all there. You can create accounts, so you can pass an address per user they can wire BTC to, query if any funds are there already (with a minimum number of confirmations), even pass the money on, to other local accounts, to remote addresses (other users or your cold wallet)

https://en.bitcoin.it/wiki/API_reference_%28JSON-RPC%29
https://en.bitcoin.it/wiki/Original_Bitcoin_client/API_Calls_list