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Play System Shock 2. It ruined Bioshock for me. Bioshock is a POS to me because I was spoiled by System Shock 2.
Anyone mention Deus Ex yet? GOTY on Steam for 10$. RPG shooter with one of the better plots, side quests, exploration, characters, multiple endings etc I've experienced overall.
All the quirky original stuff like Psychonauts, Braid, Portal etc that I can immediately think of has been mentioned.
Then there's all the games that you must play because if you haven't then you've never been in contact with another human before (Starcraft, Half-Life, Halo, Zelda, Mario).
Then there's the games that just did everything right, generally while inventing their own entire genre or being the outstanding examples in a small genre, yet fall under the radar sometimes. I don't see a lot of these already listed, excepting Shadow of the Colossus and something else I probably missed. XCOM. You MUST play XCOM at some point (1992? DOS). ChronoTrigger, the only JRPG I ever liked. Ground Control, a solid predeployment RTS. StarControl 2 was amazing with what it was. Planescape Torment (>Baldur's Gate IMO). Fallout 1 & 2. Alpha Centauri (If you liked Civilizations). Freespace 2. Operation Flashpoint.