I just bought a simple digital camera not that long ago, too. Most these days seem to use their own proprietary rechargeable lithium ion battery pack. I specifically got it because it takes AA batteries since any lithium ion battery has a fairly finite lifespan and I will likely not need to buy another digital camera for quite a few years, and that style of battery pack may not even be available at that point. But I digress.

Well, the first part of the solution definitely would be to store the camera with the batteries removed.

However, depending on how much you use your camera and how often, let me toss out another option to going the rechargeable route. Besides the excellent suggestion to use a good quality rechargeable NiMH like the Sanyo Eneloop, another option would be lithium AA's, like the Energizer e2. High performance, long shelf life. Can be expensive if you buy them at the drug store, but much more reasonable if purchased online.

Actually, so far, I'm totally fine just using alkaline AA's and just making sure I remove the batteries in between uses. That one thing could be all you need to do.

Good luck!