Ok now that I have my shiny new comp up and running (Thanks to people that helped me out here) What are some Computer games you would suggest?

Do you have any particularly favorite genres?

Guess it would be nice to note that huh? lol

RPG
Action/Adventure
RTS
Occasional FPS
Occasional MMO

RPG is by far my favorite.

STALKER: Shadow of Chernobyl and Call of Pripyat (the first and third games of the series) are quite good, combining some of the exploratory elements of RPGs with the gameplay of a shooter. You could think of them as non-linear FPS, set in a really spooky environment. There's also Metro 2033 which is somewhat more linear, but it's got really impressive high-end visuals if you want to give your machine a real workout, and its atmosphere is even creepier than STALKER.

As for full RPGs there's the Witcher, which seems to be one of those love-it-or-hate-it games, but I quite enjoyed it. It wasn't as predictable as most typical fantasy stories, and the combat was quite involving. Then there's Mass Effect, a really great RPG that hits all the right sci-fi tropes. Definitely worth playing, especially for fans of Bioware in general, though the sequel wasn't as good imo. There's also Dragon Age: Origins (and Awakenings, but I haven't played this expansion) which was very good and reminded me a lot of the old Baldur's Gate games in many ways. Like the Witcher, it tried to avoid some of the more obvious fantasy cliches (while hitting others like an iceberg. )

Mount & Blade: Warband is excellent if you want something a little different: a hybrid between RPG and medieval combat simulator. Castle sieges, physics-based damage, commanding armies of hundreds of archers, pikemen, and cavalry - it's very light on story, but if you've ever wanted to be part of a full-on melee, this is the game.

For RTS games there's actually a http://www.gamesas.com/index.php?/topic/1158205-rts-games/ going about them right now.

I have less time than I have suggestions, really...

The STALKER games are nice indeed. Alternatively you can whip out your copy of Morrowind and torture your PC with the Morrowind Graphics Extender.

For an 'action/adventure' game Mirror's Edge is very nice.

I got Stalker free with my video card, I don't really care for it.

Played Dragon Age and Mass Effect.I have been considering The Witcher 2, Will I miss much if I don't play the first one?

Hard to say at this point, but I'll bet some characters will be making a return, so it's possible.

Overlord is fun. A hybrid/mix of RPG, strategy, action, and adventure elements. Some light humor, and a bit of replay value (but not over-much). Minimal choices-and-consequences.

Hellgate: London (with the Revival Patch) is insane fun. A new Revival patch is coming out in the next month or so (at least, I hope), I'm really excited for it. Yes, the game is now single-player only. But that's okay, I like single-player games. There are some other great mods for the game that I'd recommend using. It's a hack-and-slash RPG. Some say the plot is threadbare and barebones, but I was able to enjoy it aside from one or two gaping holes and a few odd leaps of logic. Everyone says the game is rubbish, but I don't think so. Best $2.50 I ever spent. I want to make a Cabalist Evoker for my next character, the gear looks sweet. And, uh, shooting lightning and fire out of my hands is going to be fun. You can also play the classes that use guns, switch the camera to 1st person, and treat the game as an fps. I played the Templar faction with a Blademaster class in 3rd person, so my experience is a 3rd person hack-and-slash with melee weapons.

Trine was fun, though it is a pretty short game and has limited replay value for single-player. Very pretty visuals, I ought to replay it soon.

Psychonauts. I got 90% through it on the PS2. PC version has way faster loading times. Hilarious game, very creative and has pretty tight gameplay.

Gothic 1. Even with patches and mods, it can crash now and then. I enjoyed playing it (er, with god mode). It's an Open World RPG, but the class and skill system is tied more to the faction you choose than to free-form character creation. No level-scaling means it's easy to get your butt kicked early on - but in later levels, you'll be mopping the floor with your enemies. If you like G1, you will probably want to get G2 to play.

Titan Quest is fun, and you can still play multiplayer on the Gamespy servers. It's a hack-n-slash RPG set in ancient times (Greece, Egypt, Babylon, Asia) with a whole smorgasbord of mythological monsters and legendary items. The community patch is a must-have, and there are a few nice mods for it, too (especially for freeing up the camera). It is a very long game, and you can go back to previous areas and fight the respawned enemies and bosses to your heart's content.

Majesty. An rts game even I can play! Um, but sometimes I need cheats. All my heroes are such cowards.

I have several other games that I bought and still need to play, so I can't really comment on my personal experiences with them.

I would strongly recommend Portal because its just that good.

Battlefield Bad Company 2 is a great FPS which I think is quite easy to get into if you play the singleplayer before you go online.

I'd suggest some RPGs but mine ideas have been suggested by others above me.