To review my original description:

Safe:
  • .jpg
  • .jpeg
  • .png
  • .gif
  • .mp3
  • .ogg
  • .mp4
  • .wma
  • .avi
  • .mkv
  • .pdf (?)

Unsafe:
  • .doc
  • .xls
  • .ppt
  • .exe
I haven't considered the album-art download script. Whether those can be dangerous is a good question - are they really file-side? I was assuming the player searched using the meta-data available within a trusted resource... MS Office documents, I most certainly agree, should not be copied. As to DVD-menus - I don't remember any of the file types I listed supporting it. WMA and MP4, maybe? Never liked those...

The problem with the GIF is that it's data format is pretty much the same as an ASCII text file. So is a batch script. Windows trusts that what you download is a GIF file. Perhaps unfounded...
I'll test this later (giving an executable a .gif extension) - do you perhaps mean the hidden extension "feature" in Explorer? Whoever thought that thing up deserves no compassion.

The problem is not *that* there are streams; but the problem is that by default Windows has a laissez-faire attitude towards what is executable and what is not;
The reason why DLL files in particular are a danger is that they tend to be loaded early and by ‘trusted’ programs. E.g. your Microsoft Office will load riched.dll (a library for the Office rich text editor), so any malware that wants to load its main (malevolent) payload would simply attempt to inject this into such a DLL file.
I didn't mention .dll files due to those being unnecessary for an average user to transfer between computers, but they certainly fall in the same category. However, if I understand this correctly, the injection would have to be in the main file (riched.dll, not riched.dll:malware.dll), making streams irrelevant to that specific case.

Also, I looked it up, and copying a stream over to a filesystem that does not support it (or generally doing anything with it with a program that is unaware of it) will destroy it.

At any rate we are veering off into the realm of the academical arguments. My point is that you cannot trust a file based on (false) assumptions on the file type.
Indeed we have, but I truly am curious how wrong my advice was. To adjust it, Beirut: Make sure that the files you copy contain what you expect them to contain (are valid images, music, etc.) and that their extension really is what you expect it to be. If you're unsure, Linux (and Unix, probably) has a "file" command, which allows you to check what type a file is, detecting it even if the extension is wrong/missing. If you don't mind spending time on it, also check the metadata - I'll check if there's an easy way to do that.