I totally agree with the previous answers. Digital zoom is a technical gimmick by which the pixels are simply amplified in size to give the impression of zooming in.
In almost all cases, it is something to be avoided, and should certainly not be considered when making a new camera purchase.
Having said that, however ... I've been amazed at how good it CAN look (sometimes). I have a Canon S3is, which has 12X optical and 48X digital zoom.
A month or so ago, I became intrigued with the antics of a squirrel hanging out in my backyard and raiding the birdfeeder every chance he got.
I began shooting his performances from inside the house, through a bedroom window, hand-held, using the 12x zoom.
Then I set up my sturdiest tripod, mounted the S3 on it, and experimented with the digital zoom.
Yes, there's a lot of digital noise, and yes, it's too contrasty. But ... well, You can see the results for yourself on my flickr page. (
http://www.flickr.com/grimitz)
Scroll down to one of the two "belly flop squirrel" images.
Like I said before -- don't let the absence or presence of digital zoom affect a purchasing decision. But, sometimes, it can be fun!