real.geizterfahr: Uff... Lots of recommendations. I'll look into them later today. Just a few comments on some of the mentioned games:
Red Faction - Played it years ago. One of the few games I prefer to play with cheats. God mode on, weapons cheat on, go!
NOLF - NOLF has singleplayer? All I know about NOLF is 4 player splitscreen and lots of monkeys with rocket launchers ;P
AvP - Played every AvP game. Story is very basic, but gameplay wise they're what I'm looking for.
Spec Ops: The Line - Already played it. The only military shooter I own. Loved the story, hated the gameplay :P
Doom 3 - Doom 3 has the same "problem" as almost every id shooter: absolutely no story. At some point you'll ask yourself where you are and why the f you're fighting all those demons. I thought RAGE could be an id shooter with a story, but...
RAGE - ...all I got was an id "light" shooter. Good mechanics and the typical "Why the f am I doing this" feel that every id shooter has, but it's missing the non stop action of other id games. Traveling those distances and the stupid search for sidequest takes to long. And when you finally arrive at some location, you got five minutes of shooting before you have to travel to the next spot.
I'll have a look at some of the other games later today. Hard Reset and Singularity look like fun games. Shadow Warrior and Rise of the Triad do look ... strange :/ Especially Shadow Warrior looks like Jade Empire on drugs. Undying and Painkiller could be worth a look. And... I totally forgot about FEAR! This game caught my interest when I was on a "little girl with long black hair is doing creepy things" trip (saw Ringu for the first time back then). But somehow I never played it.
Some great suggestions so far.
I just realized, unless I missed it, no one has mentioned Quake 4. The engine is virtually the same as Doom 3 so the look is all around the same but there are a lot of nice touches that (as fun as it is) Doom 3 doesn't have. Just an example, very VERY early on you are hunkered down with your squad and your commander tells you to go track down a medic and bring him back. It's not really a story but it's a kind of a mini-mission (among many) that D3 was void of. The cool thing about finding the medic is that he is on the other side of the field so you need to duck and run from wreckage, foxholes, and burned out buildings to get to him and get his ass back.