A camera usually supports just one type of battery either a disposable battery or a rechargeable one. The exception is cameras that are powered by standard AA, AAA or similar batteries. In most of these cases disposable and rechargeable batteries can be used interchangeably.
There are two battery types:
disposable batteries: can only be used once. They usually have a standard size and shape such as AA, AAA and so on. You can buy these batteries at most stores and once they are empty you simply dispose them (please help keep the environment safe and clean by disposing batteries only to special battery disposal containers).
rechargeable batteries: can be used multiple times. Some rechargeable batteries have a standard size and shape such as AA, AAA and so on. Such standard size batteries can be used anywhere that a disposable battery can. More often than not however rechargeable batteries have a proprietary shape and are compatible with just a few specific cameras. Once a rechargeable battery is empty you can place it in a special charger that will recharge it. The time it takes to recharge a battery, the number of times it can be charged and the life time of the battery are dependant on the technology used to build the battery.
There are pros and cons to using disposable or rechargeable batteries. The main advantage to using a disposable camera battery is that you can always buy a few to have with you to replace the ones that are empty and you can always get one in a store close-by in case you are stuck with empty batteries. The disadvantages to using disposable batteries are the cost of buying new batteries every times your batteries are empty, the capacity (in most cases a disposable camera battery will not last as long as a good rechargeable camera battery). On the other hand rechargeable batteries require only one purchase. When the camera battery is empty you can simply place it in its charger and after an hour or so you will have a fully recharged camera battery. The disadvantage is that if you run out of batteries during a photo shooting session or somewhere away from home or a power supply you can not just buy another camera battery. The solution to that problem is to buy one extra camera battery and to always carry it with you fully charged.
If your camera uses standard size batteries such as AA or AAA you can have the advantages of both disposable and rechargeable batteries. You can always use disposable AA or AAA batteries with the camera but you can also get a rechargeable AA or AAA camera battery and use it when convenient.
Rechargeable batteries technologies:
Different technologies are used in building rechargeable batteries. Look at the camera battery itself to find out what technology was used in most cases it will be written on a small sticker on the camera battery or somewhere on its packaging. The following are the most common technologies and some of their pros and cons:
nickel cadium: one of the oldest technologies. These batteries are inexpensive, they can be recharged fast and many times before they lose their capacity. On the downside they have a low capacity and have a 'memory effect' - a 'memory effect' means that the camera battery can not be recharged to its full capacity unless it is first fully discharged. This can be problem since in most cases you will want to make sure your camera battery regardless of its current state is fully charged before going on a photo shooting session. Some charges solve this problem by first discharging the SONY CYBER-SHOT DSC-F77A camera battery and only then recharging it to its full capacity.
nickel metal hybrid: this technology is an improvement of nickel cadium. These batteries capacity is much higher up to 50% more. Although it still has a 'memory effect' it is less noticeable than in nickel cadium batteries. On the downside these batteries can be charged less times before losing their capacity and they also discharge faster when not in use.
lithium ion: A new technology that solves many of the nickel technology problems. Lithium ion batteries have a higher capacity than even nickel metal. They have no 'memory effect' at all (and thus regardless of their current state they can always be recharged to their fullest capacity). The downside is that they are more expensive than nickel batteries.
lithium polymer: the latest technology. These batteries have all the advantages of lithium ion and more. They have an even higher capacity and can also be easily manufactured in any shape or form. This allows for much smaller and lighter high capacity batteries and for batteries shaped to better fit the camera design.
In conclusion when choosing a camera and considering what batteries it uses you should first make a choice between disposable and rechargeable batteries. If you choose to get a camera that uses rechargeable batteries you should try to choose a PANASONIC CGR-S007E camera battery that uses the latest technologies like polymer or lithium unless you have some special considerations.