Well since topics like this just get everyone naming their favourite games, Tetris DS. The online is still big (lots of n00bs and pros) and with the ranking system, you play people around the same skill as you.
It does really depend on what kind of game you wanna play.
Mario Kart pretty much takes the bone seeing as its almost everyones favorite. But if your a hardcore Shoot em up player the Metroid Prime Hunters is the Game for you.
But if your a puzzeler who likes a challenge then Tetris would be a great pick. Or if you just like lazing around all day watching the clouds go by the Animal Crossing it is.
You can never go wrong with the classic battler; Pokemon.
I have all those games (Altough I lost MK) except for tetris, but I think I could imagine what its like.