I remember as a young kid dropping a metric ton of quarters into SF2 arcade boxes. Many gloriously wasted hours (and dollars) playing that game. :D
Wolf3D introduced me (and probably a good portion of the people here) to shooters back in the glory days of DOS. It put that small game developer, id software, firmly on the map and started them on the way to becoming a major force in game development.
Quake was the first game I spent more than 24 consecutive hours playing. All hail the "crash-and-burn" after the caffeine wears off. :P
Red Faction was way ahead of its time. When it came out, destructible environments were a pipe dream for many game makers. GeoMod made it a reality. Too bad the engine never caught on with other developers.
Unreal Tournament was the first game I played competitively. Spent a good number of years playing the classic, made a lot of friends and a few haters, and never regretting a moment of it.