For the obvious; Solitaire, Mahjongg, so on.

Otherwise, you could try these:

Amnesia: The Dark Descent

Antichamber

Stanley Parable

Audiosurf

Boson X

Broforce

Contraption Maker

Katawa Shoujo or Everlasting Summer if you're into interactive novels. Both are free (Everlasting Summer is available on Steam as well)

S.T.A.L.K.E.R.: Shadow of Chernobyl

StarDrive

Transistor

Bastion

If you're lucky, all three Mass Effect titles

Halo: Combat Evolved

OFF (it's a free RPG, download here )

Cortex Command if you don't go full-mongolian on it

Dwarf Fortress (It's free, but the learning curve is a cliff. It's REALLY REALLY REALLY steep. But it's so worth it for the hilarity - for a taste of what can happen in Dwarf Fortress, look up Boatmurdered.)

N64, SNES, GBA emulators (Free, and technically legal as the games are, by now, abandonware)

Fraxy (Free!)

FTL: Faster Than Light for a good roguelike

Rogue Legacy

Genetos (Free!)

Jets 'n Guns GOLD (seriously go for gold if you can find it, it has more content and is hilarious)

You COULD try Just Cause 2

League of Legends/Smite/DotA are MOBAs that have an ultralow graphics setting for older rigs

If you can dig up a joystick, Mechwarrior 4

If you got a mouse on hand, or are feeling particularly adventurous, there's Osu! which is a free rhythm game similar to Beat Agents on NDS

RollerCoaster Tycoon 1, 2 are CERTAIN to run on your computer, but you can also try the third (p. sure all three are available on GOG)

If you're feeling oldschool, OpenLieroX is a fun couch or online multiplayer game if you got friends. It's free.

Re-Volt

VVVVVV (yes that's the name of a game. Look it up. Great game)

Yume Nikki if you feel playing a more abstract, sandbox game (it's free)

Zineth, if there's still a download somewhere (Free)

If you feel like making starships, there's Battleships Forever (Free)

There's also Spore/Darkspore for a cutesy evolution game with planet-busting bombs later on

Might edit post later to add suggestions.