This question gets really tricky if I drop some of the nostalgia choices (Golden Axe, Fighting Force) or my recent "hooks" (Awesomenauts, Terraria, Don't Starve). And I don't even game that much!
I'll have to go with Worms 1. I remember writing down condensed strategy guides from gaming magazines to my notebook before I even had a PC to play them on. Later came failures trying to "carry" a pirated version in a bunch of floppy disks to my 486 beast. I can't put a finger on what exactly fascinated me about the game, but I think it was a mix of turn-based strategy, awesome characters, battling my friends, crazy weapons and oozing charm + humor in every aspect of it.
Never got any good at it, hah.