If you want to run multiplayer games for friends or family over your LAN, or an Internet based game open to the world, bear in mind the bandwidth restrictions. Anything except a turn-based game will be nigh unplayable if the server is on a low speed dial-up connection! High-speed cable connections are required for servers for more than a few people - bear this in mind when setting up a server.
Multiplayer shooting games such as CounterStrike, Half-Life, the Quake series and Return to Castle Wolfenstein require large amounts of bandwidth for large games, but they are easily playable for several people over an Ethernet LAN. To run them for many people, you should use a dedicated server (i.e. a machine that is used for this purpose and no other) - small games can use a listen server, allowing you to set other responsibilities on the same machine at the same time.
Strategy games and turn-based games can often use dial-up connections. Bear in mind this can be quite slow at times, but try out your favourite game to see how it runs on your machine and connection. There's no hard and fast guide to these things, other than the obvious: be sure to always read the manual and check your network settings carefully.
