Just a few games from the top of my head:
Criminology (aka Crime Scene)
Developer: White Birds Productions
Video:
http://www.youtube.com/watch?v=jygMqWU00K0
LifeSigns
Developer: Spike
Video:
http://www.youtube.com/watch?v=eZKUk3xBAKI
(The game is heavily story-driven. You do perform operations, but you will spend more time going round the hospital talking to various characters.)
Miami Law (aka Miami Crisis)
Developer: Hudson
Video:
http://www.youtube.com/watch?v=j1IDXPWWknc
(There's a mix of 'action' and investigation. I think there's enough investigation segments for it to be an adventure game. The 'action' segments feel like minigames anyway.)
Unsolved Crimes
Developer: Now Production
Video:
http://www.youtube.com/watch?v=nPQamu7KKBc
Not out yet, but hopefully sometime this year:
AGAIN
Developers: Cing, Tecmo
Video:
http://www.youtube.com/watch?v=QjiRB0shYcs (English!)
If you're thinking of including import titles as well, then that's going to be one big list lol. I made a list of Japanese adventure DS games from a couple of years ago, and it's pretty out of date. But if you are planning on also including Japanese games,
than I guess that's a good place to start.