It depends on the games you want to play. Most games work fine with the client behind a firewall with NAT, unless you are blocking outgoing ports. If your default rule blocks all ports, you would need to open the ports for the individual games you want to play.
You may also run into problems with multiple client machines connecting to certain online game servers, as the server sees all the connections coming from your external interface on the server, which probably has only one IP.
If you mean hosting a game, you should be able to play LAN games, but would have to forward the required game ports to the box behind your firewall that acts as the host for outside clients to acess it. Some games also require ports for the server to communicate with a master server.
Hope that helps.