Trace Memories / Another code *
hotel dusk room 215 *
touch detective 1 & 2
Broken Sword, Shadow of The Templars *
Last King Of Africa
Secret Files-Tunguska *
Syberia
Theresia
Undercover: Dual Motives
Runaway 2 The dream of the Turtle
(This is an ok port to DS, some thought has gone to making it work BUT the touch screen controls during the dialogue are HORRID, you WILL pick the wrong dialogue choice 80% of the time no matter how careful you are).
Ankh
(if you don't mind foreign language with english subtitles. I don't think this was ever released on the DS with english voice over (maybe its not that great a port, the game is just an ok adventure game on the PC)
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Almost all of these are worth a little investigation. Those with an asterix (*) are ones I enjoyed most.
A bit more experimental/acquired taste games you might look at,
Flower, Sun and Rain
Lux Pain
They revel in their weirdness and people seem to either love or hate them. Lux Pain isn't really a game though, there's not much investigation or even any gameplay, its more of a visual novel/anime.
I do not recommend Jake Hunter Detective Chronicles or Unsolved Crimes, steer well clear of Unsolved Crimes.