Since it only got one mention, I have to give a second vote to Yoshi Touch & Go. That's probably my most played DS game. It's thoroughly thoroughly addicting in my opinion.
The PowerPro-Kun baseball games are also really easy to get into and arcadey fun to play. Try out the Korean one (Powerful Pro Yagyu Begins) for a pure stripped down game without the story mode.
Homebrew is great for pickup & play type games, too. Extreme Onslaught, SpoutDS, Everlasting Love/Tomorrow Hill, Pizza Worm, DSquares, No Place To Hide, Rubber Bands, Word Up!, Twist and of course Touchdown! The Alien Attack. Those are all great quick play games that I keep on the main menu of my G6 cart. AmplituDS and Gioioso!, too, but you said no rhythm games.
...word is bondage...