I compared the GOG.com version of Another World to the SNES version, and in the SNES version there is almost all the time some background music playing, but in the GOG.com version it is mostly missing. Is this a bug? I'm running a 64-bit Windows 7.

I don't know if it will help in your case or if the music is missing or not but . . . using RunFirst to set the affinity of Divine Divinity fixed a sound problem for me. It is a free program for setting affinity via the shortcut target path.
Look at this thread for a link to down load and an example of how the target path would look after adding the FirstRun command to the existing path. , , =)
Edit : If you have a single core CPU, don't use this file.

Thanks. I also found the [url=http://en.wikipedia.org/wiki/Another_World_(video_game)#15th_Anniversary_Re-Release]following information[/url] from Wikipedia: "The game does not include Interplay's extra music, but it does include the extra level, as well as the added enemies and hazards from the console versions along with updated sound quality."

There are Mp3s you can download from GOG after you buy the game. I'm inclined to think they where CD tracks for the 15th anniversary edition. I don't know how they could be played appropriately during the game.

These files were on a bonus CD and were just an addition. There is no in-game music (and never was).

I see. That's interesting.
My assumption is bogus.

This is just a guess but I believe the downloadable soundtrack comes from the MegaCD version of the game, which (I believe) had a RedBook soundtrack.

Yes, the soundtrack included as a bonus here is the BGM of the Sega CD/Mega CD version, but not this version. That version also included new redbook audio for the cinematics, and the sequel, Heart of the Alien. I don't know if Heart of the Alien was made by the same guys.

From watching the making-of video, I learned that the music that comes with the 15th Anniversary Edition was originally composed for the game, but Eric Chahi ended up not using it in the game itself (except for the intro and outro) because of technical limitations. So it's more of an extra bonus.

Nope, Heart of the Alien was a unoffical sequel created by Interplay.