Most (all?) digital cameras include digital zoom; for some low-end cameras, it's the only zoom they have.
The amount of digital zoom in still-photography cameras is modest, usually around 3x. Among DV (digital video) movie camera, digital zoom has gone out of control, so that mine, for example, boasts of 200x zoom. That's made up of 8x optical zoom times 25x digital zoom; fortunately, an option in its menu limits the max zoom to 40x -- that's a mere 5x digital zoom. I've seen a camcorder boasting 840x digital zoom. Yikes! (Beside the text are photos taken with the DV camcorder at 1x, 8x, 40x, and 200x.) At 200x zoom, photography is no longer possible: the image stablizer can no longer compensate for hand-shake, and the auto-focus can no longer find sufficient contrast to focus on.
Some photographers say to switch off digital zoom altogether, because using digital zoom is no different than enlarging the image in PaintShop Pro -- an action that degrades the quality of the image. They are correct, technically. But not artistically. For photography is art.
With all the talk of megapixels and lenses with good glass, I think photographers sometimes forget that it's the quality of the image that matters, not the image quality. Grainy photos; blurred photos; underlit and overlit photos; photos with the "wrong" white balance -- these are not mistakes but art. (Not that all such photos are necessarily art, of course -- some are mistakes!)
* Minimum 3-megapixel resolution.
* Correct subject matter.
* Necessary for compostion.
* Limit the digital zoom to the resolution.
In my experience, there is no problem adding 2x worth of digital zoom to photographs -- if needed to get the composition correct. Yah, it could be fixed in PaintShop Pro, but I want to create the picture when I snap the shutter, not fix it later in the digital darkroom.