What are the most recommended circuits and equipment for testing AA and AAA alkaline batteries used in household items?

And are there any useful applications of weak batteries which still have a little amount of power in them? Like an AA battery with voltage and current measurements of 1.20 V and 0.2 A. If they can even light an LED for several hours with that power, it'd be good.

I'd also like to know What is the definition of a dead battery and when it is recommended to throw them out without wasting its remaining power?