Doom
The granddaddy of the first person shooter, the original ass-kicking demon-slaying 3d slaughterfest, Doom is a franchise that demands respect even in the hallowed halls of /tg/.
Minimalistic in plot, Doom is easy to grasp; you are a Space Marine (no, not the 40K guy, a jumped-up soldier who is sent to fight on other planets, so closer to the Imperial Guard) stationed on Mars. Somehow, demons break through into our reality and slaughter everyone else on the planet. Your job? Fight your way to where, you hope, there's a ride off of this rock, and make bloody mincemeat out of everything standing between you and salvation. Standing in your way are armies of zombified fellow marines and eggheads, fireball-tossing imps, hulking flesh-eating demons, cyborg-demon monstrosities, and various other nasties who want to kill you horribly. Good luck. You'll need it...
Although not the very first of the FPS genre (that goes to its predecessor, Wolfenstein 3D), Doom was definitive to the genre, so much so that "Doom Clone" was the standard nickname for many years afterwards. And, for the time, it was incredibly dark and gory. To put it in perspective, there's still people playing it and hacking around with the source codes for it to make funner games to play - there's even a monstergirls modhack being churned out, complete with hand-drawn artscenes and a complete revision from "kill the demons" to "fuck the demons into submission".
The original Doom was fast-paced and bloody, but not afraid to take breaks for scares, either; there's some really creepy levels in there. Doom II, meanwhile, was even faster-paced, a circle-strafing explosion-rich gorefest that defined the game in the eyes of its fandom. In the early 2000s, Doom 3 came along, following in the example of Doom 64 (a little-remembered Doom game on the Ninendo 64) as a slower-paced, creepy, almost Survival Horror themed game. Meanwhile, the next Doom is due out in 2016 and can basically be described as "3d Brutal Doom II", with advertised features like ripping enemies apart with your bare hands and having to stay on the move to avoid being torn to shreds.