Ultima Online (Pre tram)
Star Wars Galaxies (pre sony buyout)
EvE Online
all of these games had/have awesome PvP (i do not like AI ... AI can always be beat one way or another a human LEARNS and adapts)
All the simulations rFactor .. Il-2 (just got but boy am i having a blast doing a campaign right now) Race, GTR etc etc are awesome fun when racing and such online
Xbox Forza Series is just amazing ... if they could come out with a Forza for the PC (ranks customizations etc) i would never ever leave my house and prolly die in 2 months from lack of food and a life haha
FPS ... Call of Duty series for sure wins with Arma being a close second for realism
RTS ... Company of Heroes is good Starcraft is good ... Men of war is bad ass
Sports: Madden was good now its just meh ... NHL (ea sports) is a ton of fun online now with the be a pro mode ... my friends and I each play our normal positions and make our pro as close to possible as real life (me im fast with some nice moves (dangler) and a slow but accurate shot) it is intense online with 12 people playing

that is what i can think of now ...
However both games went south and went "carebear"