MMO - FFXIV for right now, though I have such fond memories of FFXI I could never go back, it's time is done.
racing - I don't know for PC, the Forza series overall though
Action - what is an action game? Like Rogue Legacy? Or like Dark Souls?
Sports - Basewars! : D
RPG - Suikoden 2
Shooter - Mass Effect series
Strategy - Crusader Kings II
stealth - Skyrim
So many games cross genres these days. They combine elements.