I have a Sony MiniDisc Walkman player, here is a link to it:
http://www.sonystyle.com/is-bin/INTE...c_NetMDWalkman

A minidisc holds like 5 hours of music, and never skips. I have an armband to put it in for when I run or work out at the gym. It comes wth software you put on your computer that lets you either burn CDs onto minidisc or transfer MP3s off your computer onto your minidisc.

Advantages:
-cheaper than an iPod (much, much cheaper. My Walkman cost $100).
-discs are cheap
-never skips
-small size
-longer battery life than an iPod
-will scroll name of current song across the screen
-you can purchase accessories like speakers, etc.

Disadvantages:
-a disc holds less than an iPod
-software will only let you transfer an MP3 up to three times (this is because of the anti-piracy laws). I don't know if that is the case with the iPod or not. There are ways around this though. Renaming files, etc.
-no backlight on digital display (although you can get a more expensive model with a backlit remote).
-discs needed (only comes with one)
-doesn't have a radio tuner (I don't know if the iPod does or not).

I like my MP3 player a lot. I found it to be a much cheaper alternative to an iPod. I think the main advantage to the iPod is that you can buy one iPod and keep all your MP3s on it, so all the music you could ever want is always with you. Since I really only use my MP3 player when working out, I find that making "workout discs" with like 50 songs on them is quite enough for me. I don't take my MP3 player everywhere, but if I had an iPod, I imagine I could. Good Luck!