Few games filled me with despair like the first Silent Hill. The game is a constant downward spiral into worse things and situations, with no release or good ending in sight. That feeling is still with me when I think about the game, more than 20 years later. I could never muster the strength to finish it a second time.
The 7th Guest/The 11th Hour duology gave me similar vibes, but the games weren’t as good. I guess the poor gameplay coupled with the gratuitously gory FMV contributes to the feeling, but it also left me feeling kinda dirty. Silent Hill is a much better experience in all aspects.
Xenosaga Episode 3 is another. After all your characters went through, after all the pain and betrayal, there’s no happy ending. A far cry from Xenogears and especially the Xenoblade games.
Oh, and if you think you won’t find despair in cutesy platformers, play Klonoa (the PS1 original or its excellent Wii remake).