Tend to take 'refuge' in classics which I often revisit anyway. If am in the adventurous frame of mind, I'll go for The Longest Journey (the first not sequel), Syberia (1 & 2), Blade Runner, Gabriel Knight 3...

If am in for some fun in inflicting some damage and blowing things up and stuff: GTA San Andreas, Mafia, Hitman, Godfather... those alone never fail to do the trick.

I enjoy playing WWII games most (my favorite genre)...

... but...

... when I'm anxious or feeling stressed I enjoy playing Dragon's Dogma Dark Arisen. Sometimes I'll just enter the game to wander the hillsides and watch the sun rise and fall.

I do the same with Red Dead Redemption -- although not quite as often -- just ride a horse through the back country and pass the time.

Doom 1/2, Heretic, OMF 2097 Borderlands 1 for just mindless kills. I'll also load up an Elder Scrolls or Fallout game if I want to enjoy scenery and lose myself in a character.

Xonotic - Smashing through bots or friends is always good.

Not so much a game as music https://www.youtube.com/watch?v=MhJbvagcV6E

That's some easy listening right there, I tend to find myself closing my eyes to this music!

Unreal Tournament, the flavor depending on the mood.

2004 most of the time, sometimes UT3. Ocassionally 2003 out of spite because the world seems to ignore that the game exists. Ironically, I play the classic UT the least.

Just shooting the shit out of inhuman/godlike bots gets me relaxed every time.

There are so many....here's a few of mine.

First those played out of bed:

Blood 1/2
Daikatana(oddly enough)
Doom 1/2(classic) and Doom 3/expansions
Duke Nukem 3D/Forever
Mass Effect series(I've played these so many times i've lost count, same as with SS 1/2)
System Shock 2 and the FMs for it(also SS1 to a lesser extent)
Thief 2/1(still need to complete the first one)
Unreal 1/2(still need to finish the end of game 2)

Then those played in bed/on the go:

Phoenix Wright series
Professor Layton Series

Via other people reminding me of them here:

Beyond Good & Evil(HD version is amazing)
Freelancer(still need to beat it, though)
Big one: Hidden Object games(multiple series....currently one Haunted Legends)
Monkey Island Games(played all but the telltale ones)