I'd like to also put a vote in for Contact, it's a great game that people miss. Others that I can think of that get missed often:
- Lost in Blue (there's 3 of these but they are pretty much the same. Stranded kids must get off deserted island.)
- Time Hollow
- Trace Memory
- Hotel Dusk: Room 215
- 999: 9 Hours, 9 Persons, 9 Doors (just had the sequel announced for 3DS/Vita NA release!)
- Okamiden
- any of the Phoenix Wright games (I especially loved the Miles Edgeworth Investigations, but I do love Edgeworth!)
- Chibi-Robo: Park Patrol (not for everyone but I love the Chibi games!)
- Retro Game Challenge
- Soul Bubbles
- The Dark Spire (haven't put a ton of time into this one but my husband LOVED it)
- Shin Megami Tensei: Strange Journey
- The World Ends With You
- Little Red Riding Hood's Zombie BBQ (I think this might be available on DSiWare now?)
- Solotorobo
- [Import] - Dai Gasso Band Brothers
There's a crazy mix of games there, but I have put more time into my DS than any other game system I have ever owned. I love the way I can just pick it up and go, the rechargeable battery doesn't restrict me like the old game boys did (I put a fair amount of time into my SP as well before the DS came out), and companies really didn't know what to do with the dual screens at first and a lot of really great games were created, just because companies were willing to work with new IPs.