Depends profoundly on the person. For some people, it's a silly notion that games could help at all.
Other people will want to experience darker things that coincide with their mood and let them perhaps think about emotions they feel in a different way. Braid comes immediately to mind in this case. And really, every person should be required to play Braid anyway.
But maybe they just want to feel some joy and happiness, in which case games like Animal Crossing or The Sims are nice.
Maybe they want a game where they can sit back, relax, and focus more on the story and such than on the difficulty - to take the pressure out of gaming. A lot of RPGs fit that nicely and older point-and-clicks like Grim Fandango are phenomenal for these purposes.
Perhaps they want to marvel at random surprises, comfortably explore an endless world, and build vast monuments as large as their imagination. Minecraft would be ideal there (highly recommend Peaceful mode for a more tranquil and sublime experience).
Or perhaps they just need to vent some frustration. Plenty of FPS and beat-em-up games to choose from there.
The thing I'd be most likely to aim for though is niche games. Being part of the "in-the-know" crowd with respect to cult, niche, and indie games can really bring a lot of joy to a person's life, just as any feeling of inclusion in an exclusive group. Games like Braid and Minecraft are nice options as are historical goodies like Grim Fandango (though if you go that route, be aware that there's one very brief point in Grim Fandango that requires a bit of software to artificially decelerate your processor).