We bought our daughter a MP3 player - I think it was a Genius (like the mouse brand). It takes a AAA battery and is a PITA! We are constantly buying new batteries for it because she looses the rechargables (didn't come with any rechargable batteries either).
Also, beware of the format that they will play, a guy at work thought he got a good deal on a player, but found that it only played MPEG4s, which he did not have the software to create and upload to the player.
Our other daughter has a Sony, which has a usb in one end like a flash drive, which you plug into the computer to charge and upload songs, but the songs have to be in some wierd Sony format and needs the software that comes with the player. It also has a radio as well, but I suspect it was rather expensive - my husband bought it for her, and didn't tell me how much it cost him...
I have an iPhone, which has the iPod Touch functionality, but I don't like listening to music too long with those ear thingys, they get a bit annoying and I don't know how some kids can handle having them in their ears all day- but there again, maybe I'm just too old for that sort of carry-on?