There's an enormous thread about DS adventures, but since it's so huge and indiscriminate, it might be worthwhile to have another thread for good ones, specifically
The Phoenix Wright/Ace Attorney series is worthwhile. Some may argue that it's overhyped by now, but most AG fans seem to enjoy it. I recommend starting with the first one and working your way through the whole series.
I find Trace Memory/Another Code and Hotel Dusk to be somewhat obnoxious and underwhelming in their presentation, but both are pretty solid adventure games that use the DS in clever ways.
Professor Layton is fun, and the puzzles are great, but the puzzles are so distinct from the story that it doesn't feel like much of an adventure game.
I haven't played the Touch Detective series, but most reviews seem to place it around Meh+. Better than nothing, but check out the others first
