I once rode 2 miles on a flat tire. I was on an isolated section of trail by myself and it was getting dark, so I rode back to more populated area where there was a bike shop. The wheel was not damaged, although it might have made a difference that it was the front wheel so there was less weight on it.

But, changing a tire is not too difficult. This is pretty good overview.

http://www.youtube.com/watch?v=i5K-DXt9djA