Thanks for all the responses, folks. I'm away on vacation so I'll need to check take in all this advice later. I could have sworn I looked for all possible GFCI outlets when this problem first occurred and tripped/reset them all. I would assume that if one of them was the cause of this problem, that it would also be dead, but they all seemed fine too.

I'm hoping it's not frayed cords.

And I'm interested in tracking down the source of Tony's hum, too! As previously established, my house also has a weird noise that I've asked you folks about. Funny thing is, I couldn't hear it the other night, but I can't recall if the absence coincided with the outlets going dead.