A number of what could be termed "Adventure" games are available for the DS, in Japan anyway.
Personally I would recommend both the "Kenshuui Tendo Dokuta" games.
They play a lot like Phoenix Wright crossed with Trauma Center.
Of course, unless you read Japanese, most of the story will be lost. Saying that, though, I know ZERO Japanese and I managed to follow the stories and complete both games.
That was before I realised
www.gamefaqs.com had partially translated walkthroughs for both games.
You can take a look at the second game on its official (Japanese) website...
http://www.dokuta.com/
