The most common complaint about digital cameras is that they are tough on batteries. The need to power the  LCD display  continuously is given as the main reason for this heavy drain. It's a fair comment, but it is not the only or even the main reason for short battery life.
Note here that I am talking about fully automatic, compact digital cameras, the ones you can carry in your pocket - the most common type sought by Mr and Mrs Everyman. These comments may or may not apply to cameras used by serious photographers.
Every time you switch the camera on you will hear a whirring sound. This is the lens being run forward into the operating position. This is not a "for free" operation. Some of your precious battery power is used in the process. Then, as you take each photo, a similar sound is heard as the auto-focus motor moves the lens into the taking position. More battery power. As long as the camera is switched on, the auto-exposure mechanism is adjusting the shutter speed and aperture to suit the ambient lighting. This doesn't consume much of your battery power, but it is going on all the time, for as long as the camera is on and ready for action. You zoom in to get a closer view - the zoom motor draws more power from your battery. And finally, when you have finished taking your photos, another whirring sound takes more out of your batteries as the lens is retracted back into the camera body.
Couple all of this battery consumption with that needed to run the LCD display and is it any wonder that 2 or 4 AA cells don't last very long.
If you are looking for a camera that will not cost a fortune in batteries, chose one that does not retract the lens when switched off, and preferably one with manual focus and zoom facilities.
My early Digicam would take about 50 shots on a set of batteries. My new single lens reflex camera has taken 1150 shots and is only on its second set of batteries - a better than ten times improvement in battery life. The new camera does not move the lens when turned on, auto focus can be turned off, and the LCD is only on when I want to review the shots I've taken. My new camera cost about 50% more than an equivalent compact camera but having saved the cost of about 20 sets of batteries, I am well on the way to making a profit!