I think that would be Dark Forces on PC.

I think it was Wolfenstein 3D, Duke Nukem 3D, or Hexen.

The first Doom

Can't remember if it was Doom 2, Halo CE or Ghost Recon because I played all three the same year, but it's one of those :P

Goldeneye 007- N64.

Turok: Dinosaur Hunter (N64). Rented it and loved it, but didn't buy it until a couple of years later.
GoldenEye was the first one I bought. Man I miss split-screen multiplayer with friends!

wolfenstein or duke nukem, but the most memorable was probably goldeneye

3D? If so:
Medal of Honor on PS1

If not:
Sunset Riders on SNES

If any game that involve shooting as it core counts, then:
Afterburner on the Sega Master System

Hey man, what did Contra ever do to you?

COD MW.