You mentioned Doom so there is hope
I have always been an FPS guy. There are some other types I do like to play, but generally not much in the way of MMO and such. Also, I have been gravitating toward "old school" stuff, or maybe what you might call retro. Somewhere along the way these games seemed to slip for me with the newer versions. Sure they look great, but I like to play games and stuff, not watch cutscenes over and over.
Anyway, if you haven't checked it out, GOG is absolutely awesome for the old stuff. You can fill up with lots of great games there for great prices, and they are all de-copy protected and set up to run on modern systems, even the really old stuff. Like Doom. You know, DOOM - from 1993! I got on their mailing list and I just wait for the sales to come around, then I buy what I want on sale. Then you are getting great games for absurdly low prices, we are talking a few dollars here. I just bought on sale the entire Leisure Suit Larry collection (3 games) for $5.47 total.
Here is some of the great stuff I have bought from GOG:
Doom and Doom II (DOS old school)
Quake, Quake II, Quake III
Duke Nukem
Return to Castle Wolfenstein
Serious Sam First and Second Encounters
Aliens VS Predator
Unreal, Unreal 2, Unreal Tournament 2004
You can spend a lot of time shooting up stuff with those, what great times.
On Steam I have:
Bulletstorm
Duke Nukem Forever
Half Life (best game ever hands down), Half 2 and all the associated episodes
Unreal Tournament 3
Other games I like:
Far Cry, Far Cry 2
Soldier of Fortune I and II
Bioshock
Just to prove I don't have a one track mind, I have a few non FPS that I like.
Roller Coaster Tycoon
Goat Simulator
Train Simulator
I guess the newest game I have is Grand Theft Auto 5 although that is on my Xbox. But the PC game should be the same. Loads of fun.
I also like flight simulators but don't have time nowadays to get into one of these and spend the time to figure it all out.