To make something useful out of 'dead' batteries I've been building Joule thief circuits. These circuits are very easy, cheap and fun to build plus it gives me a little bit less bad conscious when going to the recycling bin with the batteries. Watch this BigClive video to learn more.
Below are pictures of one variant. It has a small 3mm green led (salvaged from a broken printer), a hand-wound coil, a resistor and a transistor.
The batteries here came with my first ever (analogue) multimeter. They are 32 years old!. See the date code: 84-04. They still can drive the little led. Amazing. I think running this little green led is a good way to use the last energy stored in these beautiful and truly long-life batteries.