I´m totally new on this site and so far I love it:).I found this site because I felt like playing UT all of a sudden. You know this acute attack comming out of the blue. The thing is that I want to find a really cool game that I have´nt played before. I´ve played a lot of Deus Ex (AMAZING game- try it if you have´nt) and Unreal Tournament, just to give you a feel to what I´m into, but I know those games and concepts a little too well. Are there any other non-linear First person shooters apart from the DX series please let me know.

they say system shock 2 is pretty good.
I also enjoy farcry 1 and 2.

Deus Ex is pretty unique in its style - it's mostly FPS with a few RPG elements mixed in.
The only games I can think of which are comparable would be System Shock 2 and Bioshock. System Shock 2 is much less linear, but Bioshock is easier to play.
If you're interest in even less linear gameplay, you could try something with stronger RPG elements, like Arx Fatalis (here on GOG!), or Oblivion.
Edit: You also mentioned being a bit too familiar with the UT/DX game concepts. For something a little off the beaten path, you could also try:
* Military action games, like Rainbow 6: Vegas, or Call of Duty 4. These aren't too demanding, but give you a little bit of a chance to play with tactics and different weapons.
* Heavily scripted linear FPS games, like Half-Life, Far Cry, or FEAR. These don't offer much flexibility, but are a blast to play.
* FPS games with RTS elements, like Giants: Citizen Kabuto (GOG!), Wheel of Time, or the (now free) multiplayer-only Savage: Battle for Newarth.

i think Stalker could fit in. It has rather sandbox structure, shooting aint easy but u have quite good choice of guns and lots of sub quests.

STALKER. Maybe Far Cry 2. But STALKER is totally awesome.

stalker and fc2 are pretty intensive games, so be careful. try a demo first.
if your computer can't run crysis, it can't run farcry 2, as they use the same engine

Well... I can't run Crysis on high but I do run Far Cry 2 on maximum graphics (and damn it looks nice)

Yes, Far Cry 2 runs on a heavily modified and optimised version of CryEngine2 Ubisoft call Dunia, I also get better performance on it than I do on Crysis.

thanks for mentioning this, i'd never heard of this game before but i just check out some videos and it looks SO AWESOME
now to find it on amazon...

Vampire the Masqurade Bloodlines kind of fits, its less of a first person shooter though it does the non lineir deus ex styles area's very well. It does have guns in it but they are harder to use then most other shooters. They work on a similar weapon skill system to deus ex but I never leveled it so can't say if they start feeling like a real shooter later or not. It does have melee and magic that you can use, and the melee works fairly well. The Story telling and envirments are great in the game though.

You could try an old (since we all here are goggers) game called Anachronox. It's a blend of FPS and RPG, has a futuristic setting and actually has a sense of humour. It came out in 2001, and used a (very modified) quake 2 engine, which was old at the time already. : ) Interesting that the same company that released this game, Ion Storm, released another famous game too, Daikatana. :D

Soldier of Fortune 1 and 2 is nice. DO NOT BUY PAYBACK. EVER.

I don't think they are exactly non-linear... but they are good shooters anyway.
By the way, you can also try "Boiling Point", the game is buggy as hell but with the latest patch I remember it was kind of fun.

Yeah, Boiling Point was given pretty bad scores in the reviews (usually games are reviewed out of the box, not with patches), but the patches made it really good.
And Just Cause. That was one of the few games I remember where I actually liked the bugs.