Rechargeable batteries are the ones which can be charged multiple times. Such devices are a collection of one or multiple batteries, which employ electrochemical reactions running on several chemical combinations. They work on the principle of reversible reactions, and are used in applications such as cars, laptops, flashlights, mobile phones, cameras, etc. Laptop batteries need to be recharged very often, after their charge is exhausted. Cell phone batteries usually get charged in 3 - 4 hours.
Ni-MH or nickel metal hydride batteries are the best options available in the market these days. These serve as a good choice for flashlights, and remote controls of toys and TV. They can retain their charge for many months.
Uniross Hybrio: This Ni-MH battery is termed as hybrio and is manufactured by Uniross, a French organization. A set of four would approximately cost you USD 12. They are equipped with 1900 mAh (milliampere-hour). This unit signifies the total amount of energy reserved by a battery at one time. These devices are available with brand names such as Uniross, Again and Again, and Ultralast. You get them fully charged at the time of buying, just like any alkaline battery.
Sanyo Eneloop Batteries: These nickel metal hybrid batteries are manufactured by a Japanese company called Sanyo. You can recharge them for about 1000 times. It takes approximately 4 hours and 2 hours to recharge AA and AAA batteries respectively. Their capacity is about a maximum of 6 months of reserve. R6 or AA batteries can store approximately 2000 mAh and AAA can store approximately 800 mAh. A charger that can be connected with a USB port is also available, and they can be charged at the time of buying.
Duracell CopperTop: They are standard alkaline varieties, and are available in the sizes of 9 volts, C, D, AAA, and AA. These do not get exhausted in an idle state, hence they work best for smoke detectors. Self discharge rate is very low, and they can retain their charge for a long duration.
E8GE 1000: These are the latest ones which can store up to 2100 mAh. You can recharge them up to 1000 times. Their charge can be stored for a period of almost 1 year, and if its kept idle for this entire period, it will still be approximately 85% charged. You can use them in devices like CD player, digital camera, remote controls, and clocks. They can also be fully charged at the time of buying.
Rayovac I-C3: These batteries can be charged in just 20 minutes, up to approximately 1000 times. I-C3 stands for In Cell Charge Control, which results in a very less charging period. AA type of these batteries can store up to 2000 mAh, and a pack of 4 will cost USD 10. They are equipped with a fan, which prevents their heating during charging. There are 2 charger types available for these devices: PS5 can charge 2 Rayovac batteries, while PS6 can charge up to 4 of these.
Depending upon the application, you can choose your rechargeable batteries from the above varieties.