I think for most people the biggest considerations are the form factor (how big it is mostly) and the zoom. They say the best camera is the one you have with you, and you will carry a small camera more than you will carry a big one generally. There are plenty of pro photographers that take pictures with a smartphone when they're not working because it's so convenient.
The downside of the smartphone of course, is the other aspect, zoom. If you are going to take outdoor and especially wildlife photos, you can't get enough zoom. I personally use a Canon point and shoot super-zoom camera. I find it a pretty good compromise between my smartphone camera and an SLR.
This is the newer model of my camera: Canon SX30IS
. 35X optical zoom and it takes great pictures. If you're not concerned about being able to zoom a long way and would like a smaller camera or want to spend less money, something like the Canon PowerShot ELPH 300 HS
might be a nice option.
Both have image stabilization and can shoot 1080p video by pushing a single button. They both also have an HDMI output which makes it very simple to display your pictures and videos on your HDTV which is a great way to look at them. The SX30IS has a viewfinder (so you can hold it up to your face instead of looking at the LCD) which is important to some people and an articulating LCD which is nice if you're trying to shoot something at an awkward angle. The ELPH doesn't have this stuff and only has a 5x zoom, but will fit in your pocket.
Don't worry about megapixels. Anything over 5 or so is more than enough unless you're planning to make poster sized prints of your photos. Megapixels is a great marketing tool because it's simple and easy to understand but it's not a measurement of camera quality.
Don't worry about how simple/complicated it is. All digital cameras these days have auto mode where all you need to know is 1) turn on the camera 2) press the shutter button. The more complicated cameras aren't any harder to use than the most basic ones if you use auto mode.
Pro photographers mostly use Canon and Nikon and it's more of a religious argument than a rational one which is better. Sony/Samsung/etc. make fine point and shoot cameras as well. I am a Canon fan but not for any good reason.
In the end, as I said, what's important is the form factor that you want and how much zoom you need.
[This message has been edited by Levi Forman (1/24/2012)]