FPS - Hard to say, but I'd have to say Doom or Quake. Those were the first games start the whole FPS craze. It's notable that Quake is also the first game where players actually needed a dedicated GPU.
Tactical Shooters - Rainbow Six 3 & Vegas, Ghost Recon Advanced Warfighter 2 or Brothers in Arms: Hell's Highway. Those are true tactical shooters if you ask me. Call of Duty is a fun series, but it's more of a run and gun shooter and there aren't much in the way of tactics since you can't command anyone. True tactical shooters involve the ability to command your teammates around the battlefield with maneuvers like flanking and suppression fire etc.
Racing - Forza Motorsport 2. Gran Turismo may be the granddaddy of all racing simulators, but Forza is the new and improved daddy in the block. The physics and damage are very nicely simulated and are actually very close to real life.
Role-Playing Game - The Elder Scrolls IV: Oblivion. Hands down the best and most addicting RPG I've ever played. World of Warcraft can go kiss my asian ass, but Oblivion is just awesome. The level of open ended gameplay and interactivity is just astounding. Because of this game, Bethesda Softworks is easily one of the best developers in my book. Heh, I have over 200 hours of Oblivion logged in my XFire account. Yes, it's that fun.
Real Time Strategy - Company of Heroes. A graphically amazing game with insanely simple gameplay. Commanding troops is very easy and everything has a very tactical sense to it. Relic did a great job with this game and I definately can't wait for the expansion pack.
Overall - Hard to say, but Oblivion definately has be hooked. I've never found such a game where I could get sucked into it for hours and not stop. It's not a perfect game, but it's damned close.