I'd have to go with the first Max Payne. That game just oozes atmosphere. It had the perfect soundtracks to go along with Max's depressing tone and makes you feel really sorry for him.
Second would probably go to the KH games. They're bitter sweet and know how to hit you in the feels.
What are yours? (Note: It doesn't have to be depressing, just as long as the game is captivating and has a strong tone.)