I played a ton of Nintendo DS back in the day, though I think the only game I ever really got into the multiplayer for was Mart Kart DS, which was incredible both online and locally, the latter of which could host eight (!) players. Man, that was a riot, especially because the only time we could gather enough people to fill out the entire lineup for that was in public venues. Strangely enough, I think my second favourite game for the system after that was Clubhouse Games. It was like the prototypical iOS game, except before iOS, and without annoying in-app purchases.
Other games I remember enjoying:
Dragon Quest V
Mario & Luigi: Bowser's Inside Story
Picross
Puzzle Quest (this is on every platform now)
The World Ends With You
Other games I remember enjoying:
Dragon Quest V
Mario & Luigi: Bowser's Inside Story
Picross
Puzzle Quest (this is on every platform now)
The World Ends With You