Three reasons:

Save money, lessen environmental damages, reduce our use of natural resources

There is a myth that rechargeable batteries and battery chargers are too expensive and will not pay for themselves.  This is not true at all, the cost of a rechargeable battery is nearly the same as a disposable.  Universal battery chargers that can charge anything from AAA through 9V typically range from $5 to $40.  Most modern rechargeable batteries can last up to 1000 recharge cycles, this may be a lifetime of battery use for some people.  Depending on how many batteries you use a year, the savings could be very significant.

Each year Americans buy 3 billion batteries, less than one-fifth of these batteries are rechargeable.  Every American throws out 8 batteries a year, added up this ends up being 180,000 tons of batteries that end up in the dump.  14,000 tons of these are rechargeable.  Even though newer alkaline batteries contain far less mercury than previous, they still end up in the environment.  Instead of looking for new natural resources to make batteries, old ones can be recycled.  Recycled batteries can easily be broken down to make new batteries and more.