Nanashi no Game (or the Nameless Game) is a really cool hidden gem for the DS. Unfortunately only released in Japan, it has a story very similar to that of The Ring, involving a haunted game that kills the people who have played it after 7 days.
The atmosphere is really good especially for the DS, with some beautifully crafted low-poly models and textures. The game switches from 3D when it is the real world and 2D when we have to play the haunted game, which is unique and makes clever use of the DS's dual monitor.

The story kinda sucks and I wish there were more puzzles or action (it is more or less a walking simulator) but it's worth playing just for the atmosphere.