I'll happily recommend
The World Ends With You to anyone who owns a DS. It's an immensely clever RPG by Square Enix that does an excellent job of capitalizing upon the DS's more outlandish traits without ever descending into being a simple tech demo. It should be pretty cheap by this point, having come out for the original DS back in the dark days of 2008.
The narrative is a glorious story of what happens when you drop a fairly standard misanthropic amnesiac JRPG protagonist into a setting where failure to become a worthwhile human being will kill him. What follows is raw, fashion-mongering, vending-machine-dropping, pin-collecting, precision-snacking brilliance.
Oh, and in spite of what the box and Wikipedia think, the game has excellent multiplayer. The game runs separate but co-dependant combats on each of the DS's screens and it's a bit much for one brain to handle, so you'll tend to leave the partner's screen running the fairly good AI mode. Switching the AI off and having a friend use half the buttons to manage the top screen while I used the stylus to fight on the bottom one is some of the best fun I've had with a DS. Surprisingly effective too.