Hi Brenda and welcome to the Q&A Board,
There are two types of Image Stabilization systems for digital single lens reflex cameras (in-lens, in-camera). There are pros and cons to each. You can read about them here:
http://www.digicamhelp.com/camera-logs/11/dslr-is.phpI recently bought my first DSLR. Based on my shooting style, I opted for image stabilized lenses, though they tend to be more expensive at this time. I use telephoto lenses and like to photograph wildlife, including birds in flight. It's important that the image in the viewfinder be stabilized. This is not the case with in-body IS.
Compact digital cameras are especially prone to camera shake because they are small, many do not have high shutter speeds or usable high ISO. Some don't even have viewfinders so users hold the camera at arms length.
I think you will find differing of opinions among seasoned DSLR users as to whether IS is a must. For many, it hinges of the speed and focal length of the lens. But I find it of great value, wouldn't be without it and many others feel the same. IS is being incorporated into many more cameras and lenses than before.
Before buying any lens, you need to find out the "focal length multiplier" of the camera. So, unless you're buying a full frame DSLR, the focal length of the lens will be longer than specified (see comments below by Deb). You may find my DSLR dilemma blog helpful, where I share some of my findings about the world of DSLR cameras. It's an interesting journey, and while similar to using a film SLR, there is quite a bit to learn:
http://www.digicamhelp.com/camera-logs/11/Please don't hesitate to ask if you have further quesitons. All the best with your new DSLR!
Related reading:Image Stablization:
http://www.digicamhelp.com/camera-features/camera-parts/image-stabilization.phpFocal length multiplier:
http://www.digicamhelp.com/camera-logs/11/flm.php