Long time ago, there was a game called Quake, and there was a group of people that came out with a mod for it called Team Fortress. With the success of Half-Life, Valve too saw the area of opportunity that online gaming was. They knew that a simple deathmatch won't be enough, so they got their hands working on a multiplayer addition for Half-Life, which was called Team Fortress Classic.
In Team Fortress there are two teams, Red and Blue, and each one has an objective. It may be to capture the other team's flag, command control, or escort something for example. In the game, you can play for one of the nine different classes, with their pros and cons. These classes as a whole have skills that will help the team in one way or another. The classes are scout, sniper, soldier, heavy weapons, demolition, engineer, spy and pyro. Each has its own unique weapons. The game formula is a hit, and you can still find plenty of TFC servers around. If you own Half-Life you can get this game for free. Otherwise it has a $4.99 price tag on Steam, Valve's official store. Even with TF2 out, some people still prefer TFC, so you should give it a try.