Well, that was weird: on a hunch, I went to my Edit Preferences page, and found that somehow my "Do you want to be notified via email when you receive a private message?" had gotten changed to "No".

Edit-- This is interesting: I have a list of back-and-forth PM's, and when I click on that it takes me to the latest one. I'll let Anu know; maybe he can find out what's causing the difference.