I'm surprised nobody's mentioned the Ultima series yet; Although I havn't played any of the games, I've heard a lot about them and how big a thing they've been.
Anyway, here's my list and explanation of each.
○Halflife -Solid sci-fi first person shooter, amazing moddability.
○Starcraft -Still one of the best real time strategy games out there.
○Diablo 2 -Although I eventually got bored with it, I still poured hours and hours into this game, and had a really fun time with it. Plus there aren't that many free online RPGs (no pay-to-play).
○Warcraft 3 -Continues on with an already well-known storyline, still one of the nicest looking 3D real time strategy's, and the addition of Heroes added a new twist on gameplay. Also, very very cool unit and map creation.
○Unreal Tournament -My first introduction to first person shooters on the PC many, many years ago at a friend's house. Fast-paced, constant action and energy.
○Unreal Tournament 2004 -Great action I enjoy from the first one, with the introductoin of vehicles and many new game modes.
○Sim Tower -Not as complex as the Sim City titles, but still plenty to do and a lot of fun. Rather obscure title, not many people have heard of it.
○Halo -One of the few first person shooters that I enjoy the single player storyline more than online play, good ol' PC mouse and keyboard controls.
○Grand Theft Auto 3 -Brought the classic GTA games to 3D, great storyline, a lot of fun.
○Grand Theft Auto: Vice City -Improved a lot over GTA 3, introduced new gaming elements (shooting out tires, jumping out of cars) and vehicles (Motorcycles, helicopters).
○Battlefield 1942 -First game based around first person shooting and vehicular combat.
I'm sure there are more I've forgotten, but these are the ones I remember off the top of my head.