Mario Kart is good but the online is plagued with cheaters and don't even bother going online if you don't know how to snake. If you can find a copy cheap, which is nearly impossible unless you get it from a family member or a garage sale then go for it but I wouldn't pay full price for this title. Which is why I don't own it yet.
Anything out of the main Pokemon series, avoid the spinoff games as they are generally terrible. I haven't played a Pokemon ranger since the first one, it was way too difficult and all that drawing circles will damage your touch screen for sure if you don't have a screen protector. I recommend Pokemon Black or White just for the speed of the game, it is so much better than the other titles and makes the other games feel ancient and slow. You can usually get Pokemon games on sale for 24.99 on Amazon in fact I think there are some on sale for that price now. Since Pokemon D/P/Plat/HG/SS are considered the last generation of games you might as well just jump in with Pokemon Black or White.
My main DS library consists of games like the Square Enix RPG's, Dragon Quest and Pokemon. Also some Atlus RPG's but not all Atlus games are good so check reviews first. Definitely look at the Trauma Center series.
Retro Game Challenge is also a very good game, and can be found cheaply these days, don't miss it. That along with Geometry Wars.
If you have a DS Lite don't forget about GBA games either, assuming you don't already own some, there is a big sale at Gamestop right now as they are phasing out GBA games, so be sure to pick up some good ones on the cheap!