I agree, Another Code (released as Trace Memory in North America) is an excellent game. It makes good use of the DS technology for some of its puzzles, too.
Phoenix Wright: Ace Attorney is also a very good adventure game on the DS. It’s becoming hard to find, though. 🙁
Here’s a game to keep an eye on — Osawar Tantei Ozawa Rina http://www.adventuregamers.com/gameinfo.php?id=796
So far an English version hasn’t been announced, but they have an English website up, which seems promising.