Games like Myst DS, Hotel Dusk: Room 215, Trace Memory and Professor Layton and the Curious Village. Asides from those four are there any other DS adventure games? Also I heard Phoenix Wright Ace Attorney was an adventure game, but I thought it was a court room simulation. Which is it?

Ace Attorney is both, and it is the very best game on DS second only to Planet Puzzle League. :DDD

A remake of the original Broken Sword was released (in Europe) for the DS and Wii a few days a go.

Aw, and here I was thinking we were gonna talk about good ol' adventure for the 2600

Phoenix Wright saga is awesome. You should give it a try.

Dont bother with it, just play the PC version.
All the best adventure games have already been mentioned, and yes, Phoenix Wright is the first port of call if you want more adventure on the platform. Adventure games are about the characters really, how they build and change; reacting to the situation they find themselves in. The Ace Attorney series is a seminal example of this and should be played by any adventure enthusiast.

Legend of Zelda: Phantom Hourglass seems to be a good action-adventure game.

another good one, if only it was ported to DS (keep the same graphics though!)