My brothers and I used to get together for multiplayer game night awhile back, and here's a list of games we used to play. I'll try to trim it down so it's mostly co-operative gameplay.
MMORPGS / RPGS
Warhammer Online - MMORPG -Easy fun for a large group, as it's free to play up to level 10. You're able to jump right into the battlegrounds (or skirmishes as I believe they call them) right from level 1. It will auto-boost you to level 8 or something like that so you won't get entirely stomped into the ground by higher level players.
Dead Frontier - MMORPG - Zombie browser game in the form of an MMORPG. Grab your friends and complete quests in a zombie infested city. The gameplay is top-down zombie-thwacking action, but really, it's only fun when you've got your buddies with you. The last time I checked it was free, but the gameplay gets stale very quickly. Still, it's good for a weekend or two.
Lord of the Rings Online - MMORPG - The game has gone free to play. I'm not really one for these types of games, but if you enjoy grinding mobs one at a time, farming for sweet loot, and completing meaningless quests that don't really change the world in any way, then by all means, give this game a try. I had a lot more fun with Warhammer, but that was because I'm more into PvP. One thing I did enjoy about Lord of the Rings, was the ability to create your own music if you bought a musical instrument.
Dungeon Siege - RPG - A Diablo clone. We couldn't get Diablo working on our super-computers, so we played this instead. It's not the greatest, the combat is simple and you'll find major annoyances when playing with friends (like whoever gets the killing blow recieves all the XP) but it's still good for a once over if you can find the game in the bargain bin.
Neverwinter Nights - RPG - An RPG based off the D&D system. We had fun playing through a couple of custom campaigns in this one, including a Diablo remake, but ultimately, the levels get stale after awhile as there's not much more to the game than venturing into randomly shaped rooms and killing monsters. Still, it's much more detailed in terms of combat and characters than Dungeon Siege and it comes with a basic editor so you can make your own campaigns for your friends.
FPSes
Operation Flashpoint - FPS - A clunky tactical military manshoot. The most fun we had with this dated shooter/military sim was creating our own missions to run as a weekly campaign. If you're not into making your own missions, there's plenty to be found online. It easily supports a large number of players, and although the interface is annoying as hell, it can be quite fun when everyone's communicating and working together to tackle objectives. If your friends are big military buffs, consider picking this up if you can find it in the bargain bin. I'd avoid it if they're more into casual gaming though.
Serious Sam - FPS - An old FPS that throws out all the realism and just goes for non-stop action. Though the graphics are dated, there are plenty of memorable moments in this action packed FPS. The more players there are, the more monsters are generated. The levels are big and in many cases, quite clever, but they're linear, so there's very little replayability. Still, there are certain points in the game that will just blow your mind in a "HOLY F#@K THIS IS AWESOME!" type of way.
Doom - FPS - The grandfather of FPSes. Surprisingly, this game still has a large following and has many multiplayer variations. Doom Legacy, Skulltag, Zdoom. Co-operative will be entertaining as long as you all stick together (So turn off your auto-run), though if friendly fire is turned on, it can very easily turn into a death match at the drop of a hat. Still, if you can find a copy of the original game, you can easily set up a multiplayer session and have a good time.
Left 4 Dead - FPS - Four player co-operative zombie-busting action. A quality Valve game. For maximum enjoyment, I would recommend playing with friends (you do have three friends, right?). Though the levels are linear, the zombies are randomly placed and there's an emphasis on sticking together, which makes the game that much more enjoyable in the replay department. The downside, is the game is expensive and requires Steam.
Garry's Mod - FPS - A physics sand-box. Not so much a game, but a place to go and dick-around with Valve's source-engine. You'll need the original Half Life2 to play, but there's one mod for the game that me and my friends can't get enough of:
Trouble in Terrorist Town - Garry's Mod mod/FPS - Ever wondered what Clue would be like as a First Person Shooter? It's sort of like this little mod for a mod. Play as the Terrorists from Counter-Strike and try to root out the traitors in your cell. The game is all about trust, deceit, and trying to stay alive by always watching your back. A working microphone is a MUST for this game, as it's all about trying to prove your innocence, or casting false accusations at other players. Every time we played this online, we had a blast, even the gals who sucked at FPSes kept coming back for more.
Team Fortress 2 - FPS - You've already got this one, but I might suggest a certain way of playing it with friends; Set up some arena games with friends choosing random classes after each round, and you've got yourself a night of fun. Recommended minimum 4 players though.
Counter-Strike - FPS - One of the original manshooters. Buy guns, shoot enemies. It's more fun than it sounds. Round based gameplay that's still one of the top choices for LAN parties across the Americas. It's quite easy to set you and your friends to face an army of Terrorist AI scum.
SWAT 4 - FPS - Co-operative gameplay will have you thinking like a SWAT member in this thinking man's shooter. Take things slow, take precautions with each door you come across and don't go in guns blazing. This game sets you up with realistic SWAT missions in which you will have to tackle like a real SWAT team. Sooo, no Counter-Strike style run and gunning. If your friends are twitch gamers, you might want to avoid this one.
Strategy Games
Starcraft/Warcraft 2 - RTS - Though it plays better as PvP, sometimes it's fun to team up against the AI in these classic Real Time Strategy games.
Dawn of War - RTS - Plays a bit like Starcraft, but in the world of Warhammer 40,000, and with more micro-managing. We had a lot of fun with this one, both playing against each other and also against the computers. We enjoyed it up until some of the last expansions where they threw in some seriously over-powered races. But hey, most successful RTSes end up doing that one way or another.
Open Transport Tycoon - RTS - Build a business empire. The game is all about transporting goods from one location to another through by rail, sea, road, or air. Compete with friends or have everyone work together in the same company to turn your continent into a successful corporate empire. Making money and developing towns into full-fledged cities is really what the game is all about. If you're not into that sort of thing, it gets stale quickly. But, you know, it's FREE!
Kohan, Ahriman's Gift - RTS - It plays like a Real Time Civilization game in a Fantasy world. Settle cities to fund an army with which to conquer the world. This game is great Co-operative, simply because the Hard AI is VERY HARD! As in, the AI is actually good at managing it's army and will have you feeling like you're fighting tooth and nail. The combat system is neat as you custom build your regiments to include specific units in the front ranks, rear ranks and supporting ranks, opening the doors to a lot of different combat strategies. And with a host of different races and heroes to choose from, it makes the game more in-depth than your run of the mill Warcraft clone.
Men of War - RTS - One of the best Worldwar 2 RTS games ever made. It plays like a RTS, but the ability to direct control individual units to a detail of managing their inventories makes it seem like something else. It has a throng of co-op missions available, though most of them seem to just pit you up against waves of enemies. Yet, every time we played it, we'd always spend another hour or so just exchanging stories from our game.
Age of Empires 2 - RTS - This old gem can still be a lot of fun, but not for any sort of co-operative gameplay (unless you're considering dividing your friends into teams). A four player free-for-all, or custom missions still makes this game enjoyable... as long as you can get it to work multiplayer. It has a lot of trouble on newer computers
Heroes of Might and Magic - TBS - A turn based strategy game best played with only one other player (unless your friends don't mind waiting around for the others to complete their turns). It's been awhile since I've played this, but I believe you can team up against the computer which can give you a bit of a challenge. The gameplay involves building an empire using RPG style heroes to gather resources and muster an army. It's good if you have the time to actually complete a game in a single sitting.
Disciples - TBS - Spiritual successor to Heroes of Might and Magic. My friends tended to prefer this one over Might and Magic though, as the battles were simpler, therefore, quicker.
The Guild 2 - RTS/RPG - I'm not sure what to call this game, as you build your character like an RPG, interact with various town-folk, raise a family and try to build a successful business within a medieval world. There's all sorts of neat little things for your characters to do, including getting into politics, starting fights, trying to improve your standing within the community. I've easily lost many many hours playing this with friends and family, as the game doesn't have to be directly competitive if you don't want it to be, you can easily form alliances and seek to play the game in a co-operative way.
The Battle for Wesnoth - TBS - Turn based Strategy game based in a Fantasy setting. If you like hex-based games, like the old Panzer-General or Advanced Wars, you'll probably like this one. Not really a co-operative game, but it can still be fun with a friend. Any more than a single friend, and you'll probably want to limit yourself to smaller maps. The big selling point of this game, is that it's free.
Others
IL2 Sturmovik - Flight sim - A World War 2 flight simulator. You can easily set it to be as detailed or as arcadey as you like. It boasts realistic damage modeling and actual physics when it comes to flying planes and getting into dogfights. It supports co-operative play, random missions, and is quite fun if you can stand the time it takes to fly to your target. Long periods of boredom followed by intense heart-pumping action, the more players, the merrier.
Worms 2/World Party - A good party game. Though, it's turn based, the turns go by quick. You basically need to use a bit of phsyics to launch weapons of mass destruction at each other, which ever player has his worms standing at the end of the game, wins. With the ability to play hotseat, this is good fun for all ages.
There you go, a list of games I used to play Co-operatively. Some of those can probably be found cheap on E-bay if you looked, as some of them are pretty old. I've also opted not to include a whole bunch, because I'm more of an FPS guy... And honestly, how much variation is there between shooters?
