They have a bunch of game modes, and the community comes up with all kinds of wild, wild things / gametypes that you wouldn't even have thought of.
It has been over a year for me, so someone correct me if I am wrong, but they have:
Slayer - probably the most popular game. You usually play to 100 kills I believe. Whichever teams gets that first wins. There used to be specific spawn locations for special power weapons that could sway a match. At the beginning of each match there would be a mad dash to these locations. Also these modes usually have vehicles, like jeeps, tanks, and flying vehicles. A pretty standard mode, but much more epic than like TDM or something.
CTF- Big maps usually you had to Capture 3 flags to win, small maps 5. But if you got the lead you could just milk the 15 minute clock and secure the win that way. Usually an excellent game mode, probably my favorite. The guy with the flag became very slow, so you had to pick him up in a vehicle or slowly bring the flag back on foot.
Plant the Bomb- (I actually can't think of the actual name for this game mode) but a ball / bomb would spawn in the middle of the map, there would a mad dash to get it. Then you would try to take it to the enemy spawn and plant it at their base. As long as someone was holding the bomb, the bomb was invisible to the enemy team. You had to be very sneaky. If it hit the ground everyone in the game would be alerted because it showed up on your screen. Actually this game mode might have been my favorite.
Infected- was one of those community things that became a regular gamemode. One zombie infects ofthers that become zombies.
SWAT- one shot one kill TDM. Must be a headshot though. A really nice take on tdm. Pretty intense TDM mode.
Snipers-a sniper rifle only TDM mode...one of my favorite modes for some reason.
Oddball- either an individual or team game mode where a ball / skull is spawned in the middle of the map and whoever holds it the longest wins. Usually like 250-500 seconds or something. Think of everybody killing everybody, and the last man standing running off with the ball...running for his life.
There is 1v1, 2v2, 3v3, 4v4, 8v8 of just about any game mode.
The most competitve players probably play 4v4 slayer the most. I like big team games, 8v8 and mostly objective games, like CTF, or plant the bomb.
They have to many crazy game modes / mods to list. And I probably missed listing a couple key "normal" modes. I've played hockey, soccer, golf, horse, all kinds of crazy games that from time to time are just fun. The ability to play with the settings / dynamics of the game offers up some pretty interesting options.
You can also Forge. This mean you can take maps and completely redesign them. The community can build some incredible, incredible maps.
EDIT- I actually had a couple maps that never saw the light of day...but I was pretty proud of them here is a link to where I used the game recorder mode as I walked around showcasing those maps...http://www.youtube.com/user/mphfrom77/videos?flow=grid&view=0Edited by mphfrom77 - 10/30/12 at 5:35pm