Here is a list of a few sites to play bughouse on the internet. It is not a complete list, but a list of those sites in which bughouse is reportedly considered playable (at least to some degree :)

Chess.net

Free chess server. Some bughouse players play online here.

USCL

The official chess server of the United States Chess Federation. It is free to all USCF members. However, if you are not a member, then there is a yearly fee to join. Some bughouse play on this server.