- AA rechargeable (Nimh or Lithium)
Let me just add that rechargeable AA-sized Lithium-ion cells (named "14500") are 3.7 volts each, so a pair of them would fry a 2AA flashlight that's expecting normal AAs.
Also, be aware that Li-ion cells pack a huge amount of power for their size. Gram for gram, they're on par with dynamite when fully charged, or so I hear. Make sure to get protected cells, and still be careful. I'd definitely take precautions to keep them away from water or any other potential short-circuit condition.
Oh, and lithium versus lithium-ion. Lithium-ion is rechargeable, nominally about 3.7 volts.
Lithium proper, often called "lithium primaries," aren't rechargeable. They have a nominal voltage of about 1.7 volts and are relatively expensive compared to alkaline disposables. Their claims to fame include excellent performance in extreme cold, the ability to maintain their voltage until they're nearly depleted, extremely long shelf life, and lower weight than alkaline or NiMH. The higher nominal voltage compared to NiMH will make some types of lights run brighter.