My character's upper body imploded upon itself.
I thought that something I'd done with the muscle system had destroyed the rig, but after digging around I found out that the problem was really some stray animation curves on the seventh spine joint that were causing divisions by zero:
At first I thought that I must have accidentally keyed the spine joint while testing out the rig. But then I noticed that there were only curves for a subset of the spine joint's keyable attributes: only ScaleX, ScaleY, Visibility, and the three translation channels. Additionally, when I went to look at the curves I discovered that they were completely empty!
Anyway, after deleting the curves everything popped back to normal.
The thing that's really thrown me for a loop though, is how these empty curves came about. I've tried to recreate the problem but I haven't been able to find a way of making an empty animation curve accidentally.
Does anyone out there know how this could have happened?