One of the earlier FPS games in the genre. It was created by "id Software" and was immensely popular. You're a space marine that is stranded on mars where horrible experimentation with teleportation technology has accidentally opened a portal to hell. Being the bad-ass you are you decide to rectify the problem with any and all guns you can get your hands on. Killing demons with shotguns, rocket launchers, a chainsaw, plasma rifles, etc. I played the hell out of it when I was a kid. I can't wait to play this new one.

What about Wolfenstein? Doom is essentially just like Wolfenstein set in the future and instead of the Third Reich, you're killing monsters.

Doom was among the first wave of FPS games. Still pretty damn fun today.