Couldn't really decide on one single game, so I decided to ramble on about a whole bunch of games instead. Maybe you'll find something that you hadn't considered before. ^^
Mario & Luigi: Bowser's Inside Story
My favourite game in the Mario & Luigi series. Gotta love Fawful.
Phoenix Wright/Ace Attorney series
Just play them all, if you can. 1 and 3 are the best.
9 Hours 9 Persons 9 Doors
Really cool visual novel with great atmosphere, interesting story and fun puzzles. Shame there's no proper skip function in the DS version, but it's still the best version available, since the iOS version cuts the puzzles.
Rhythm Heaven / Rhythm Paradise
The game that introduced me to my favourite rhythm game series. The touch control works surprisingly well, but I still prefer the button controls of the GBA and Wii games.
Umihara Kawase Shun 2nd Edition Complete
A compliation of Umihara Kawase 1 and 2? Yes, please. I've been playing this for years now, and there's still things for me to learn and master. One of the most unique and challenging platforming game series around.
Retro Game Challenge
I love me some retro games, even if these aren't "real". Even better if you're a fan of Game Center CX like me. The sequel is great as well, especially now that there's a fan translation for it.
Elite Beat Agents, Ouendan 1 & 2
Awesome rhythm game series. Great humour and visuals. I just wish you could skip the spinners...
GTA: Chinatown Wars
Great throwback to the first two GTA games. Drug dealing is relaxing and the way you have to lose the cops by making them crash is really fun.
Picross DS
Relaxing and addictive puzzle solving. I just wish you could play the Normal mode puzzles in Free mode instead, so you wouldn't have to worry about miss-taps. Also, the DS is THE platform for a picross game.
Professor Layton and the Unwound Future
Best Professor Layton game on the DS. Fun story and characters, challenging puzzles.
Henry Hatsworth in the Puzzling Adventure
Challenging 2D platformer with fun characters and awesome boss fights. Some of the levels are kind of a grind, though.
Ghost Trick
Really nice visuals, interesting story and characters. The puzzles didn't impress me, though...
Mario Kart DS
Was great online when it was still available. I really loved snaking, as it made a lot of the more boring tracks much more interesting.
The Legend of Zelda: Spirit Tracks
Better than Phantom Hourglass, and I remember it having some really interesting puzzles as well.
Solatorobo: Red the Hunter
For some reason I really liked the world of this game. Light action-RPG gameplay. Could have been a bit more challenging. I really hope we see a sequel some day, as I see a lot of potential in this game.