There is a correlation between digitial zoom and mega-pixels. The more pixel resolution you have, the more yuou can zoom in digitally without affecting a "normal" or effective resolution.
As Big Dog mentioned, digital zoom is using the camera to enlarge and crop. I never quite got idea until I realized that it's the same thing as downloading the picture into the computer, then using photo software to enlarge the picture and crop out an enlarged part that will fit your paper (or screen). If you have low resolution in the camera, as you enlarge the picture it gets grainy. If you have more megapixels than you need, you can enlarge it quite a bit and still look good.
There are different rules of thumb, but the one I use says that going up approximately 1 paper size = another megapixel. Less that 1 (640x400) is good for a 3x5 image. 4x6 really needs 2 mps, 5x7 = 3 mps, 8x10 = 4 mps (at a minimum). If you enlarge a picture about 4 sizes then crop a 3x5 image out of it, you need 4 mps. If you crop an 8x10 out of it, after enlarging, you need about 7 mps. Some will nitpick the numbers I used, but the logic is correct,
Digital zoom does the same thing, only still in the camera. When you use digital zoom, the camera enlarges the picture to something bigger than the camera can display, then crops it to fit in the display. If you don't have enough megapixels, the picture is crappy.
So, you strike a happy medium some place. Most of the cameras you'll see in that price range had 3x optical and some number, perhaps 8x to 10x, digitial. 3x times 10x is 30x total zoom. My wife's HP is a 5 megapixel with that zoom arrangement. If I try to use the entire zoom, the picture only looks good as a thumbnail. Try to blow it up to, say, about 5x7, and it gets really grainy. However, without the digital zoom, I get a beautiful 8x10, and can maybe enlarge and crop it just a little.
I wanted at least one camera in my family with a little more zoom, so I spent a little more money, sacriced a little in the megapixel factor, and got a Nikon Coolpix with 8.3x optical and 3x digital, with 4 mps. It was just a tad over 3 bills at Sam's Club. That was 6 months ago; it's probably totally out of date, by now.
The other thing to keep in mind is that the more optical zoom you have, the more room the lens mechanism will take, and the larger the camera will be. Betsy's HP707 is nice for the pocket (although not as small as some others); my Nikon will fit in my pocet if I want to look like a dork and lean to one side when I walk.