My first new digital, a Canon S-100 Powershot, used a tiny rechargable battery exclusive to that model. It was good for about 5 minutes. Cost $75xx each. Bought 2 on ebay for $30xx each but they faded out in 6 months. Everytime I went for the camera it was dead!
It seemed to drain even if it was off.
**My number one requirement is AA batteries!
Currently I have a cheap Samsung S730 , bought 4 Nickel/metal hydride rechargable AA's with it over 3 years ago and they run the camera for ...I'm guessing here, about 30 minutes of use per pair. The camera takes excellent shots and has a big screen on the back to see what you're doing.
I always look for dials that turn when shopping for electronic stuff. I can't stand pushing them little buttons and listening to beeps. If I can't figure out how it works in the store, my next step(after AA's & dials) is picking a camera with the smallest and simplest direction manual.
I use this camera hard...it's an essential tool at my job and it's surpassed my expectations.
I might move up to a Nikon Coolpix soon just to get better distance shots, but the Samsung has served very well and owes me nothing.