Digital Zoom Versus Optical Zoom

With improvements in digital cameras over the past few years, regular point-and-shoot cameras going to 12x optical zoom, and Super Zooms going up to 20x optical zoom, most people don't need to worry about digital zoom these days.  But for those of us with older point-and-shoot cameras, the question still remains: digital zoom versus optical zoom.
When looking for and using a digital camera you want to pay attention to the optical zoom and not the digital zoom.  Why?  Optical zoom will give you a much better picture.  In my opinion, digital zoom is worthless and I rarely use that feature on my camera.
In optical zoom, the camera uses the lens to bring your subject closer to you.  Optical zoom is similar to using binoculars and is a "true" zoom.  The quality of your image remains the same as if you were not zooming in.
In digital zoom, the camera takes the image, enlarges it (i.e. zooms in), and crops it.  Your subject is not closer, it is bigger, then cropped.  Digital zoom creates an artificial zoom similar to what you would do with your photo editing software.  In doing so, you lose the quality of your image and your photo can become grainy or pixelated.
Here's some examles:

This picture was taken with my camera at 3x optical zoom.  It is the closest optical zoom my old camera will go :)  It's not super close, but it is clear.

This picture was taken with my camera at 11x digital zoom.  It is the closest digital zoom my camera will go.  It's close, but not clear.  Notice how grainy the picture is.
To recap, you want to use your optical zoom not your digital zoom if you want clear, good quality photos.