Sooo many good choices, but I have to settle on Doom. I played the shareware version when it first came out and it was an entertaining game to say the least. Now back in '08, I finally got around to playing the rest of Doom 1 and all of Doom 2, and I could not have been more entertained. It seems impossible that the first genuine stab (I'm not counting Wolfenstien and its always lit and always 6-foot high corridors a true attempt) at making a first-person game would have been the best, but there just aren't any other games that I feel like cruising around in as if I'm playing Windows Solitaire on some down-time. Somehow, Doom is just perfect.
Edit: I can't let this post go without throwing a few other names out. Just like Doom, they set out and accomplished something and accomplished it well, just as Doom did. Their only drawback is they aren't as instantly digestible as Doom is.
Heretic
Half-life
Team Fortress 2
Bioshock
Deus Ex
Jedi Knight (I can't say no to force powers)
Thief (not a shooter, but I'm counting it anyway for being first-person and awesome)
UT 2004
Borderlands
Morrowind (if I'm sneaking Thief in this list, I think this can get in too)