I find it hard to boil a dozen systems down, but here's an attempt:
Dark Souls, because it's just about the only game I can play on random, infinite loop and still find new things and try out new combos and strats
Demon's Souls, because it's got the scary and the dark Resident Evil and Silent Hill seem to have lost
Skyrim (PC), because it really is worth several trips to the wild side, and the editor randomness is better than LEGO
Uniracers, because it still rocks
Super Mario World, for hours of good fun and being the first thing played on many a Super Nintendo
Tsuyoshi Shikkari Shinasai: Taisen Puzzle-dama (SNES), for its competitive two-player fun
Deus Ex, for its stunning freedom to do things as you please
Psychonauts, for everything; mind blown
Mother/Earthbound (SNES), for being Zelda's indie hipster cousin with an attitude
Wizball (C=64), Martin Galway soundtrack, awesome satellite cat, bouncing fun, best use of limited colour since eyeshadow
Of course, there's plenty more great games out and about, but these are amongst the ones that I consider to be influental and/or timeless enough to put up in a list from the top of my head.