Deus Ex:
There is a reason that Deus Ex is often cited as the greatest game ever made. A superb roleplaying game disguised as a solid stealth-shooter, with multiple choices that actually make differences in a story you truly care about. It's fucking long, and you never get close to being bored. There are two or more solutions to every problem, and like many RPGs much of it's replay value comes from going back to see how things would change if you took a different approach. This game is at the top of my post because I believe that it is the greatest game ever made, and if you only play one game on this list (or, hell, on this thread) it should be Deus Ex.
Total Annihilation:
This game was so far ahead of it's time it is amazing. It came out half a year before "Starcraft", but if you looked at their graphics and gameplay side by side you would think it was years newer. Ignoring the mediocre story and balance issues, this game is mechanically superior to Starcraft (I will assert this to my grave, though I am certainly the minority), and playing it today it feels much less dated.
The Elder Scrolls III: Morrowind (and expansions):
This game is huge. HUGE. I've put over a thousand hours into it and I'm not sure that I've seen it all. It's completely nonlinear and utterly unrestrictive, you can spend days exploring or doing odd jobs for the populace, but you probably won't be able to pull yourself away from the deep, interesting main story. Morrowind is very much a thinking man's RPG, and it requires patience to overcome it's learning curve, but it is well worth the effort. The expansions are must-haves as well, adding hundreds more hours of gameplay. Morrowind has one of the largest, most dedicated modding communities on the internet, and you can download mods that change anything you can imagine.
Other notable must-plays that I don't have time to expand on right now include:
Star Wars: Knights of the Old Republic
Star Wars: Jedi Outcast
Half-Life
Sid Meier's Alpha Centauri (and/or Colonization)
Starcraft
Grand Theft Auto: Vice City (or San Andreas)
Portal
Red Dead Redemption