There are really too many models out there and many are designed to fit different needs. The first thing you need to do is decide what your needs are then look for something that matches it.
Personally I think a lot of people get carried away with huge number of pixels. Unless you are cropping out huge sections of your picture or making massive enlargements, 4.0MP should be enough for most casual users.
Ignore digital zoom numbers, the optical zoom is what matters. If you get a camera with a powerful zoom, try to get one with image stabilization, it kicks ass.
Go to a store and play around with some of the demo models. Some styles will just "fit" your hand better. Also decide if you want something you can slip in your shirt pocket, or a bigger camera which will require you to bring along a case. Note, many of the tiny cameras are great, but their small size may make them easier to lose or get stolen.
These and the price are just a few of the factors I look at when buying a camera for someone.
BTW If you take short videos, the Canon 1sIS probably records the best videos for a digital camera.