Please read this first for a basic camera "vocabulary" before reading this article.
In my adult education digital photography classes, people come to me with all different types of cameras. Point and Shoots (or compacts), Digital Single Lens Reflex (or DSLR), and everything in-between. A common question is: What should I look for in my next camera?
The following eight points are general guidelines I would recommend when purchasing a new camera.
Megapixels determine resolution of your images. The higher that number, typically, the better. A new camera, whether compact or DSLR should have around 10 - 14 megapixels to be useful for the foreseeable future (3 to 4 years) in my opinion. 3 to 4 years is a long time in the world of digital photography, but my seven year old Nikon D100 (6 megapixels) is still very relevant and useful.
2) Sensor Size
The larger the sensor size, the better the image regardless of megapixels. Try to balance sensor size and megapixels.
3) Raw Format
The ability to shoot raw format images is a must for your next camera. The latitude and flexibility you gain by using raw formats is incredible. For more on raw vs. jpeg formats, go here.
If you are buying your first DSLR, buy a camera "kit" that includes a camera body and a zoom lens. A Nikon or Canon DSLR kit ensures that you have a good starting point with a quality lens. In the future, I would recommend purchasing higher quality zoom, portrait, wide angle, and macro lens (in that order).
Newer compact cameras offer excellent lens quality for the price, especially with Canon, Nikon, and Kodak offerings. Check the optical zoom to ensure it fits your needs on any compact camera you consider. Stay away from digital zoom which simply magnifies your image.
5) Shutter Lag
Make sure your next camera takes the picture when you want it to. There is nothing more frustrating than pressing the "capture" button and waiting 1/2 second for the image to actually be made. (I'm looking at you compact cameras.) DSLR's virtually eliminate shutter lag and ensure that when you press the button, you take the picture.
6) Size and Portability
DSLR's are fairly large compared to their compact brethren. Depending on your needs and shooting habits, this may be very important. Newer DSLR's get lighter with each redesign. On the other hand, I have used full featured compact cameras that nicely fit in my pocket.
7) Menus, buttons, wheels, and automation
Menus on all digital cameras (compact or DSLR) are confusing and difficult to navigate. I have yet to find an intuitive menu on any digital camera I've used. This makes the physical buttons and wheels on your next camera all the more important. In my opinion, the more buttons the better. This ensures I don't need to fight a virtual menu system every time I want to change my White Balance, Shutter Speed, or ISO (for example).
Your next camera should also have a level of automation that you feel comfortable with. I personally like a nice balance between auto everything (focus, shutter, aperture, exposure) and manual shooting modes. This ensures I can be flexible no matter what situation I find myself in.
8) Other Stuff
Make sure the camera has other features that you want. I personally have no need for face detection, scene modes, in-camera effects (sepia for example), movies or sound capture, etc. However, if one of those things floats your boat, don't let me talk you out of it.
Good luck and if you are interested in my specific recommendations, please visit here.