The DS, while a great system, honestly doesn't have many great games.
Phantom Hourglass is my favorite by far; the game is excellent and a must-play handheld Zelda.
Elite Beat Agents is a unique and fun game that I recommend.
The Phoenix Wright games are supposed to be decent, but since the games are simply GBA ports and I didn't hear much about them until this latest one released (the third of the trilogy) I haven't bought any. I'm waiting for the next game, featuring more DS controls and a fresh new character.
Mario Kart is, well Mario Kart. It's fun, but you should know what to expect.
New Super Mario Brothers was disappointing for me, but others seem to like it. The game just lacked any excitement. The levels seemed boring and less inspiring than the Mario games of old.
That amounts to two games that I can really recommend.
As far as RPGs go, the PSP has the DS completely smoked. The only decent RPG I remember on the DS is Etrian Odyssey, which is a pretty hardcore old school dungeon crawler. The game does have its flaws though, such as repetition and tedium, but what do you expect from a dungeon crawler?
The PSP on the other hand has some great RPGs. Amazing strategy RPGs such as FFT, Jeanne d'Arc, and Disgaea come to mind. There are a load of normal JRPGs as well, my favorite of which is Valkyrie Profile: Lenneth, a game that holds a special place in my heart. <3
The PSP also has some other interesting games, such as MGS: Portable Ops, Killzone, etc.
Also, I love being able to just shove my MS-PRO card in my PC and uploading some videos, songs, and pictures.
Anyway, both systems are pretty decent. The DS is overly popular with everyone, which is why I just wanted to point out that the system isn't as great as some make it seem as far as it's library is concerned. Also, anyone who says the PSP has no games is blind (although it used to be true). I'm shaping up to like the PSP's library more, as it caters some game types that I simply love. However, either choice would be a good use of hard-earned money.