I did some research before buying my camera (Sony Cybershot 14.1)
I learned that more megapixels doesn't necessarily give you better photos. The "expert" writing the article said anything over 8 mp is unnecessary. He suggested looking for a higher quality lens (preferably german) and higher optical zoom. The digital zoom is not as important - it just makes the megapixles larger, but that can mean fuzzy photos.
Some cameras have lots of fancy features, but can be difficult to use because of that. I prefer a camera that has the ability to customize settings (for light conditions, subject matter, etc.) but have an automatic setting for when you just want to take some quick photos without the fuss.
I was interested in the touch screen features available on some cameras. But I read a few reviews about how if something goes wrong, or your battery is low, all your controls are frozen. Sometimes simple is better, less to break down.