As OllyM said, it's most likely they will only run iPod as that's what they've got the stuff built in for. Although if you find one with AUX or 3.5mm jack in, then you can run any MP3 player on it, but have to change tracks etc. on the player not the stereo.
I don't know of any other portable MP3 player which actually has a useable interface to interact with car stereos and stuff like the iPod does - some can act as a USB mass storage device though, except it's not half as elegant as an iPod being able to search by Artist/Song/Album/Playlist.
I've got an Alpine IDA-X100 and it's supposed to work with USB drives as well as iPods. Most players use their own proprietary interface though, of which the iPod is the most common so manufactures stick to that.
I have an alpine unit which I would assume could do anything.
Currently I have my IPOD plugged into it using the IPOD connector which runs up behind the passenger seat, and an ipod shuffle USB docking station for my GF's shuffle on the transmission tunnel. All looks nice and smart and works just great.