As I looked through my old DS games I think my personal favorite, at least out of the ones I own, is a bit of an overlooked gem simply titled Unsolved Crimes.
The game is an investigative crime drama, just as the title makes it sound. It takes place in the 70s and you and your partner are assigned murders in which there is very little evidence for normal investigators to go on, such as fingerprints or hair fibers. So you have to work with the little evidence that you have to piece together what really happened, and find who really did it from your list of suspects.
While it doesn't sound too special, the cases it provides are really interesting, and there's also an overarching case involving the kidnapping of your partner's younger sister. Some of the cases include a politician who is poisoned in the hospital he's being treated at, a college professor who is stabbed to death in his office, and women who is found dismembered in her hotel room, with her heart missing, after a city-wide blackout.
Halfway through each case there will be a moment where you haven't collected all the dots to make a concrete decision on who the murderer is, but just enough to where you might already know who it is. Your partner will ask you who you think did it, and there's no real penalty if you get it wrong (since it's only halfway through the case), but if you get it right, there's a real sense of accomplishment, and it makes you feel smart for being able to figure out who the murderer was before the case was finished.
While there's not much replay value once you've solved all the cases and completed the story, it has quite a fun and compelling ride during your initial play through. If you're ever able to find a copy, I'd definitely recommend it.