So it appears that I'm running the world's stupidest backup software on my Mac.
Last night, my "media" hard disk (with all my photos and music) failed. No problem, I have a backup. I look on the backup drive and boom, there's no backup.
Apparently this software was trying to keep the backup in sync with the original disk when I deleted files. The original disk was gone, so it made the backup match... by deleting it.
Yeah, that was real helpful. Thanks, NTI Shadow.
All that stuff can probably (probably) be recovered, since nothing else has been written to the backup drive. And I'm pretty sure the original disk can also be recovered, for a price. Still, what a pain.