I was wondering because I am in a situation where I do not have much time on my hands to play games so I am thinking about getting a handheld. I have a Wii and I only play Wii Sports on it with my family or friends. I got Metroid too but became bored of it halfway, plus I just dont have time on my hands to devote to it. The only Wii game I might get is Super Mario Galaxy and Wii Fit because I loved Wii Sports. So should I buy a DS or PSP?

get a guitar.

For me not really. I have always been more or less of a steady console gamer. I had points in my life where i gamed just a tad then times when i gamed a lot. I play handheld games on occasion but it has never been a big thing to me.

My natural advice for gaming is get a DS.

However, if you want a gaming system that doubles as a mp3 player/video player/rom case, get the psp. After you've got your mp3 collection, a few simpsons episodes on it, and every from the SNES era on it, you can still buy and play games like... well, I'll let a psp owner say good games on the system.

Though if you have no time for gaming, why buy another system unless you have 2 hours in transit where you want to kill.

Ive always liked handhelds better.

As I got older I turned to PC gaming (Age of Empires, Civilizations, C & Cs, and puzzle games). Now I use a Wii mostly when other people are around and play a lot of flash games if I am bored. Although, I do rent a few single player games and may buy some used as time goes on. I recommend getting a new minigame this year. Super Smash Bros Brawl, Mario & Sonic at the Olympics, Rayman Raving Rabbids 2 all come out this year and the majority of people that like Wii Sports should enjoy at least 1 of these games. Also, if you really want bang for your buck you may be able to find Gamecube (or PS2 or even Xbox) collections of 90s games for under $10. I bought a few such collections and am very happy with them (Midway, Sega...)

I bought 2 games for my GBA in the last year (none the year before) and enjoy using it when I travel. For example, I'm gonna be in the car for 6 hours one day next month and I will be taking it. I'll likely buy a new iPod next Christmas, sell my GBA, and buy a few games for the iPod (it already comes with 3) and never get a DS or PSP. I don't really know anyone that has turned to handheld as they got older, maybe people 30+ do that when they buy a DS for Brain Age.

You sound like you are becoming more relaxed in your gaming so it seems that a DS is more for you. Also, since there are so many copies of some of the games out there, you can get tons of used games on the DS for very little so if you get bored with a game it is not a big deal.

Im freaking old. Ive never been interested in the DS or PSP. If I were to choose one for gaming though Id get a DS.

I can understand what you're saying. I've been gravitating more towards the DS lately. Playing Sudoku on Brain Age is killer. You'd be surprised how long a good puzzle game can last you. I hear Tetris DS owns also.

If you're looking into puzzle games, check out Crush for PSP, as well as the upcoming EchoChrome.

But again, comes down to preferences. PSP is definitely leagues ahead in multimedia capabilities, but doesn't offer the same pick-up-and-play that the DS offers.
I don't really think the DS has an advantage in games, as the PSP's library looks better by the day, but they're definitely two different spectrum's as far as gameplay is concerned.