The life of a rechargeable battery depends on several things. It will depend on the type of rechargeable battery, the quality of materials used, and the device you are using the battery in.
There are two main types of rechargeable batteries. The first is nickel metal hydride batteries (NiMH). These batteries can form a memory; this means that if the battery is recharged before it is fully dead, it can eventually be unable to hold a full charge. However, these batteries are less expensive than other types. This is the common rechargeable battery when talking about standard sizes like AA.
The other type of rechargeable battery is a lithium-ion battery. These batteries cannot form a memory and hold a much more powerful charge. This is the type of battery typically found in cameras, cell phones, and other electronic devices that come with a rechargeable battery installed.
The length of the battery life is going to depend on what you are using it in and how you are using that device. Purchasing a charger that stops sending power to the battery once it's full will increase the life of rechargeable batteries. See the links below for more information.