There are two categories of rechargeable batteries: standard and proprietary. Many digital cameras use standard size batteries while others require proprietary Lithium-Ion batteries.
The manufacturer typically includes a Lithium-Ion battery and charger when you buy a digital camera using the type. Lithium-Ion batterys are not widely available in stores and must often be ordered from the manufacturer or third party when an additional battery is needed.
Other types of rechargeable batteries used in digital cameras are NiCD, NiMH and NiMH hybrid. Nickel Metal Hydride are currently the most popular because they provide more capacity than NiCDs and don’t suffer from memory effect. Non-hybrid NiMHs lose their charge when not used so recharge them if you haven’t used your camera for some time.
A word of caution: never mix different battery types.
Conditioning helps keep the capacity of batteries from diminishing. Some manufacturers recommend conditioning rechargeable batteries after every 10 or so recharges.
If you don’t have a battery charger that does conditioning, do so manually. Drain batteries completely in your camera. Once they are fully drained, recharge them.
Rechargeable batteries are good for about 500-1000 charges.