I'm pretty well covered on anything major which has been on Nintendo or Sega platforms.
I haven't played a lot of the big name Sony or Microsoft franchises (or 3rd party franchises predominantly on those consoles) from the past decade and a half though. Stuff like God of War, Gears of War, Forza, Assassin's Creed, Dead Space, Elder Scrolls. I know the latter existed for longer than that, but PC franchises are also a weak point for me - I've only really played a handful of point n click games on the hardware because I don't much enjoy it as a gaming platform.
Basically if the franchise existed on consoles prior to 2001, I've probably at least tried it at some point. If it was created after that point and isn't primarily on Nintendo hardware, there's a fairly large chance that I haven't.