Pretty much 
ALL of World of Darkness.    The best starting point is 
Vampire the Masquerade or 
Vampire the Requiem, as they have lots of adventures and support.  If you don't want vampires, then the Chronicles of Darkness line has TONS of alternate stuff, from mundane cops in the 13th precinct investigating spooky shiit, to general odd assortment of immortals and such. 
Some other games that make roleplay on its own fun =
Pasion de Las Pasiones = this game makes PvP social interaction a blast.  Even if you have no idea what a telanovela is, just run it as any TV show (heck Dexter works in it just fine) where the characters are all aimed at each other and you are good to go!
My 7th Sea (link) hack of Passion is likely more comfortable to most people, as its in the typical setting and character context of swashbuckling.
Deadlands (link) does a great job, and Savage Worlds overall, of letting characters do interesting things with social and personality.  And there is fear that actually affects characters and the world, so thats fun
Legend of the 5 Rings (current edition) (link)  is the hands down best samurai fiction you can get.   It has great rules for social, honor, and glory all outside of combat. 
There are TONS more PBTA games that do this, like LOTS.... so if you can get into PBTA, then I have a much longer list...