some of the oldies are classics..
rts...starcraft, warcraft, total annihilation
fps...unreal tournament, half-life, alien vs predator, team fortress classic
rpg... sacred, baulders gate, champions of norath, diablo
fighter... mortal combat
or some of the titles less than 10 years old are good too..
rts... planetary annihilation, supreme commander
fps... unreal tournament iii, overkill
rpg... reckoning, dungeon siege iii, dark kingdom, diablo iii, path of exile, sengoku basara, dragon age inquisition, terarria, minecraft
fighter... soul caliber 4, aquapazza
its hard to pick a favorite out of the list as i enjoyed all of them in their own way. some i have played much more than others.