1. Starcraft/Broodwar/Starcraft 2 (PC)
2. Doom/Doom II (PC)
3. Grand Theft Auto: Liberty City and San Andreas (PC)
4. Half Life (PC). HL2 didn't really grab me but the original game sure did.
5. Skyrim (PC)
6. World of Warcraft (PC) - I never played any expansions or got into high end raids, and immediately lost interest after maxing my original character at level 60, but the journey to that point was one of the most memorable gaming experiences I've had.
7. Sam and Max Hit the Road (PC). Please bring back hilarious adventure games!
8. F-16 Falcon (PC). Oh for the days of anal retentive simulations with textbook size manuals, and early head to head dogfights via null modem cables!
9. Empire/Empire Deluxe (PC). Simple classic turn based strategy.
10. Far Cry/Far Cry 3 (PC). Beautiful island setting in contrast to the usual drab warehouses, crates and urban hellscapes introduced by Doom, and this franchise, to me, captured the perfect "feel" for character movement and shooting more than any other shooter hence all the ridiculous hours I put into it.
I'm sure I'm missing a bunch that might sub in for some of these, but Starcraft series definitely belongs at the top. Honorable mentions for Ancient Art of War, the Zork/Dungeon adventure game originally on mainframes, Day of the Tentacle and Leisure Suit Larry (the first few, anyway), Castle Wolfenstein series, Duke Nukem 3D, Wolfpack and many others. I'm sad to have never played classics like System Shock 2 and Deux Ex.
Arcade games are a whole other category for me as a child of the 70's/80s. Original Asteroids is still a classic with a great interface feel and great gameplay. Defender was my personal fave but unlike Asteroids which plays great with keyboard and mouse via MAME emulation, I haven't been able to come up with a suitable control setup that I can properly play Defender with short of buying an old cabinet.