Doom II (1994) was pretty much an expanded version of the original Doom. It took the same gameplay and the same engine (I think), but added a new gun, a plethora of new levels, and a boatload of new enemies, including the infamous Arch Vile, which raised other enemies from the dead and could literally kill you by looking at you. While the original was first, this one is generally considered better because, well, it has more stuff.
Doom 3 (released August 2004) in one word: "Shiiiiiiiiiny . . . ."
Everyone's going to Hell again, only this time Hell has never looked so good! Or so freaky, for that matter. Aside from FarCry? (and potentially HalfLife II), Doom 3 may very well be the greatest graphical achievement to date in an FPS. The game, however, has a distinct "oldschool" feel--many of the monsters are reimagined versions of the nearly-unstoppable legions of Hell from the first two games, the combat is frantic, the quarters are close, and bad-ass twitch reflexes are the order of the day.
It should be noted that Doom 3 recommends 500 MB of texture memory to run the game at its highest detail level setting. It should also be noted that no video card currently available to the mainstream market has that much texture memory.