RollerCoaster Tycoon 3. It's the only game I have permanently installed on my computer(s) and had ever since it was released more than 10 years ago.

Sorry, never happened to me before.

How about

"I have no time to play"

King's Bounty series.
Prince of Persia series.

MDickie's Wrestling MPire Remix Career Edition
Saints Row: The Third
Vampire The Masquerade: Bloodlines

Spelunky

That one does happen every day. :)

Castlevania 4
Castlevania Dracula X (Vampire's Kiss in Europe)
Cybernator.

SNES games always put a spring in my step.

I dislike replaying games, so ... I can't think of any, really. Dark Messiah of Might and Magic would be a good one for me I suppose. Mostly tho, when I look at my library and have to think hard on what to play, the right answer is "Just don't and go do something else."

My thing is generally adventure games, but those don't really work for those oh, hey, look, I have an hour or two and I want to play a game times. For those times, I'll play a Super Mario Kart battle if my old console and my sister are around. Otherwise, Democracy 3 works well, or recently, the Beta version of BroForce (here's hoping that the finished version comes to Gog with all due speed!).

Hotline Miami

Bioshock 1-3
Diablo 3
Evil Genius
Doom 3

For me, when I am bored or can't find anything, first I look at my GOG library, and see if I want to play one of those, or Steam, than I go to my Wii. For me though, I go to Riven or Real Myst, or on Steam I go to Spelunky, Binding of Isaac Rebirth mostly, or Proteus.

If I don't find anything on my PC, I go to my Wii, where I play New Super Mario Bros. Wii, or A Boy and His Blob, or a Kirby game.

Hard to say. I used to open my gog games folder and just stare at it for a while with all the shortcuts staring back at me. Ever since I bought Sunless Sea I feel drawn to play it again and again...... again. I'll let you know when that feeling passes; or, I'll lose my mind and you'll never hear of it again.

If I can't think what else to play I pick one of the following:
RollerCoaster Tycoon 1 or 2
Civilization IV or V
Banished
Super Mario Bros. 1, 2 or 3