I gave this a try: It seems to be a reliable indicator when a battery is stone dead. The trick is to drop the battery vertically. Neat!
It turns out that when the alkaline in a battery wears down, it produces a gas that fills the inside. So if you’ve got a box of random batteries you want to test, and don’t have access to a voltmeter or any other device, you can simply drop them vertically a short distance onto a hard surface. A charged battery will make a solid thump sound and often remain standing, while a dead battery makes a muffled sound, bounces repeatedly, and then topples over.