I have a couple of old(er) Creative MuVo MP3 players that look like a disk to a computer. (Windows thinks it can use them in other ways, too, but that means running <shudder> Windows Media Player to talk to them, so I use them as if they were disks.) Also a Sansa Clip that looks like a disk. And there were some Sony Walkman models that behaved like disks when connected to a USB port.
The key is not to have too fancy a player. The modern ones with touchscreen interfaces and all kinds of high-resolution capabilities are usually computers of their own and need to talk to special software. Even my classic iPod can be made to look like a USB disk drive, but then they can't actually play anything that you just copy to the disk -- they need to have their internal database updated by iTunes or equivalent.