Battery charging is very different for Nickel type batteries (NiCd like in the original ICybie, or NiMHd like in the original Pleo) versus Lithium batteries (Lithium Ion like used in AIBO, or LiPoly like used in the PleoRB)
The older Nickel type batteries have what is often called a "memory effect" (which is misnamed and controversal
http://en.wikipedia.org/wiki/Memory_effect )
There is a lot of battery folklore floating around on the web, so take any advice with a big grain of salt.
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Generalization:
The old green colored batteries (NiMHd) do better when completely discharged. Avoid overcharging.
Sometimes draining down the battery and recharging it can rejuvenate the cells.
They are relatively safe to take apart and replace the cells inside (
http://bobthepleo.com/forums/index.php?topic=482.0 )
Dispose of properly. Don't just throw them in the trash.
The newer brown batteries (LiPoly/LiPO) as used in the PleoRB, do not have a "memory effect".
It is safe to top them up. It is bad to let them drain down completely. If they go totally flat, they may never work again. Pleo/PleoRB won't run if the battery is too low, so it protects the battery.
Only use the official charger. They won't fit on the old charger. Let them cool off before charging.
Don't take them apart. If they are damaged - don't use them (they are more likely to explode than NiMHd batteries if you mistreat them)
Dispose of properly. Don't just throw them in the trash.
Most portable devices these days use Lithium Polymer (LiPoly/LiPO) - cell phones, iPads, etc.