I found the problem.
It wasn't a loose battery. (good suggestion though)
It wasn't the sway bars or end links.
It wasn't the brake pads, clips, springs, pins, or calipers.
It wasn't even Britney Spears rolling around in the trunk as previously suggested.
Are you ready for this?........
It was the Catalytic Converter!!! It had apparently decided to fall apart internally. There was a large piece of what looks like ceramic flopping around inside. I became suspicious while crawling around under the car, and shook the exhaust pipe. It made some bad rattling sounds. I'd been shopping for a new cat-back system anyway, so I replaced the cat, mid pipe and muffler with a Magnaflow system. She's singing a new tune now, and not a thump to be heard.
:-)
glenn