My vote goes to the original Unreal. Best level design and music I've ever seen/heard.
Of what's in the poll, it would be a hard pick between quite a few of them, as they redefined of what an FPS actually was (I'm talking about wolfenstein 3D, doom, duke nukem 3D, half life and quake). Doom would win it...
(though I wonder what counterstrike is doing there. It had no levels to go through, and was more of a tournament style FPS, in the same vein as unreal tournament).
I'm normal ;__;
The fuck? I played Hexen for about an hour and didn't encounter any weapons whatsoever.
There were three classes, each with their own weapons (three or four for each class, IIRC). The fighter (iirc) started with just melee, which was pretty hard the first couple of hours*...but even that got at least one ranged weapon at the end.
*this depended on how well you knew the levels, as it required quite some backtracking.
For the record: I've never heard of marathon either. But if anything, descent should've been included rather than strife (another one I never knew
EDIT: if tournament FPS'es are to be included, I'd vote for UT or UT2004 as well.