I guess it would depend on the situation. I'd be most disappointed if it was a major race for me and/or something I'd traveled a long way to do-- or maybe my first attempt at a distance. But, I'm just not that serious about running and I don't think I'd be too upset.
That said-- I live in an area where it's not that hard to find a half to run. In fact, over thanksgiving weekend they do an event called the "quadzilla" which is four full (or half) marathons in 4 days.
So, if I were not in shape, I'd probably be relieved. If I was in shape, I'd probably just find another race the next weekend.
*shrug*