I'd say:
Quake (with the Dark Places source port)
Max Payne 2 (with the widescreen mod and my no hud mod)
Far Cry (with the Iron Sights mod and my no hud mod)
Fear (with the devmode mod to disable the hud)

On consoles:
Shadow Complex - Xbox 360
Dead Nation - PS3

SHIT I forgot D2!

I retract my earlier post. D2 is my ULTIMATE "go to" game.

Console: Saint's Row 2
PC: Toss-up between Duke Nukem 3d (with Polymer) or Mechwarrior 2

GTA 5
Payday 2
Infinite crisis

Don't really have a go to game per se, it's more genre's for me. When I get tired/bored of what I've been playing primarily I'll switch to something in a different genre or a 'casual' type game that I can pick up and play at any time without loss of story or anything like that. I've categorized my catalog (wish I could do that on my game shelves here) so just pick something out, or see what my friends online happen to be playing and join them for something fun if I happen to have it.

Civilization IV
Pretty mindless and I can play while watching TV or talking to people (that tends to piss off a lot of people).

I have quite a lot of "go to" games, actually. More than I can easily remember, but off the top of my head:

Dungeon Keeper 1+2
UT2004
Civ2 (I really need to reinstall that somehow)
Day of the Tentacle
Monkey Island 1+2
GTA:VC
GTA:SA
Deuteros: The Next Millennium (Amiga)
Moonstone: A Hard Day's Knight (Amiga)
Wizball (C64)
Diablo 2
MegaLoMania (Amiga)
Sly Cooper 2+3 (PS3)
Alien Shooter 2
Sacrifice
Giants: Citizen Kabuto

A lot more than those, actually, but those are the ones that sprang to mind at the moment.

HOMM 3

Definitely HoMM3!

I also re-play Little Big Adventure once every few years, as well as my all time favorite adventure games :)

Beat Hazard

Minecraft - This game is so insidious it keeps stopping me playing other games I am enjoying just to mine some more...

Any Doom engine game but Strife.

More like a game that interests me so much, I don't get round to playing other games: Dragon Age Origins (and before that, Baldur's Gate Tutu).

Well I'm pretty much only playing Sktrim at the moment so...