I don't play online myself, so can't recommend any of those. Depends on what genre(s) you like. Shooters: Painkiller (old but good), STALKER series, Crysis, Far Cry, Return to Castle Wolfenstien. RPG's:Morrowind, Oblivian and Skyrim (with mods), Witcher 1 and 2.
Adventure: Myst, Longest Journey and Dreamfall. There are lot more as suggested by others, but these are some of my favorites. Some of the really old games such as System Shock, Half Life, Deus Ex, No One Lives Forever, Jedi Knight , Gabriel Knight series, Sanitorium, Blackstone Chronicles, Seventh Guest,Wing Commander series, Prince of Persia Sands of Time (yes this last one was also a console game) may or may not be playable on Win 7 64 bit, but they are classics. Anyway, lots of info from everyone. The bottom line is it all depends on what you prefer.
Wife of Runz