Not without 3rd-party hacks, I guess. One thing to remember, though: It all depends on what sound-format your files are in. Most players will probably accept MP3-files, but some might choke on iTunes' AAC files and all of them will choke on DRM'd iTunes files bought from the iTunes Store.
I think MarkSpace's software can achieve iTunes synching for some devices, but there's no simple rule for _any_ "non-iPod", as you call it. What device do you want to use - and why not an iPod? They're great and inexpensive enough...