I've got an ipod, but only because I won it in a competition, both my teenage kids have mp3 players.
The pros of a mp3 player is that you can plug it into practically any computer and put songs on it, whereas with an ipod it is synched to one computer and you can only put songs on and take them off your ipod on that pc.
My kids have both had more than one mp3 player each as they have all stopped working in just over a year, my ipod is still going after about 3 years, although I don't tend to use it that much.
Most mp3 players are a lot cheaper than an ipod, but it depends on what you like the look of and how brand conscious you are. BTW the mp3 players by kids had were all Creative brand and they have all failed so if I was buying one, I wouldn't buy that make again.