No idea on keyboards, but the Microsoft 3000 and 6000 series blue LED optical mice last for a month or more on a single AA battery. And they track on damn near anything, including rumpled bedcovers and polished stone countertops.
As to the "best" rechargeable battery solution, a LaCrosse intelligent charger, and low-self-discharge Sanyo Eneloop NiMh batteries are the best reasonably commercial/consumer solution.
However, at least the mice, they are so efficient, any cheapo NiMh lasts a long time.