Story games?

If you don't shy away from older titles, you could try some fantasy games like Neverwinter Nights (With Shadows of Undrentide and Hordes of the Underdark) or if you like cyberpunk, than i would go with Deus Ex (thats a bit old) and the newer Deus Ex: Human Revolution or Mankind Divided. All of them are story driven.
A special mention is probably Alpha Protocol. It's a spy RPG from modern day and it's got a cool story. (Yeah, there are bugs, but which game doesn't' have them? I enjoyed it multiple times)

Of course there are many games with good stories, but it depends if you're into RPGs, Visual Novels, FPS or strategy games. Then what setting do you like? Fantasy, Sci-fi (mass effect), Cyberpunk(Deus ex), alternate history, modern(Alpha Protocol)?