What to look for in a camera?

I'm interested in buying a more professional camera. One that would blow my little 8.0 mp out of the water but I haven't the slightest clue where to begin. I obviously know the big names like Nikon, Cannon, Sony, Samsung, etc but that's about as far as I know. I'm interested in something capable of capturing natural light shots more than anything. I don't need any fancy filters or pinhole/fish eye effects. I just want something I can take pictures with and use as memories. I have no purpose of using it to promote a business or to sell images. What are the 'technical' names for some of these features.

Thanks in advance. I'll pick best answer as soon as I get an idea of what I'm doing.

Do you know much about photography? I hope I'm not going to come across as condescending.
Any camera you purchase will be able to take 'natural light' photos. Some will have cleaner high ISO performance, meaning you can shoot in darker places with faster shutter speed, smaller aperture, or both and still get decent to good results.
The simplest answer is to suggest a middle level DSLR as they will cover 90% of anything that could need to be shot and do it well. But DSLR's require time, effort, and a desire to understand how to control the camera to do what you want it to do. You could leave it on a purely automatic setting, but when you do that, you're essentially using an expensive and heavy point and shoot.
8mp is perfectly adequate for the majority of photography done these days. If you only ever put your pictures on Facebook, you won't see a large enough difference to justify the expense of a new camera. Same deal if you print pictures 8x10in or smaller.
If you're not willing to dedicate the time to learning how to use a DSLR effectively, or can't budget for it, I'd recommend any point and shoot camera by a 'big name' company. Canon, Nikon, Sony, etc. Every camera from them that you can buy new will most certainly cover most bases you would need to cover.
I'm not a DSLR snob, its a tool with a specific use, I'm actually thinking about getting a Pentax point and shoot myself for travel and underwater purposes.
Hope this helps!

Normand is correct - better photos will come from learning more about your camera and lighting conditions. Don't worry about how many megapixels a camera has, 8 is plenty.