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.
Anyone remember Duracell packages having a tester? You put a battery between two nodes, and the meter would glow up showing how much you had left. I kept that around to test my batteries, but my mom thought it was trash and threw it away. Duracell doesn't make that anymore. Is there anything similar I could find?