I'm a bit concerned about how many of you have encountered dangerous horses. Whatever happened to those horses that made them attack people?! It usually takes a lot to make an animal as gentle as a horse go against people... exceptions exist, of course, but reading these posts it sounds more like you're working with lions. Not saying anyone here did anything wrong to these horses, but in most cases, something must have gone seriously wrong in these animals' lives. I mean, I've known quite a few horses that would start nipping trying to get treats if they weren't (gently!) put in their place when they first got saucy, and some horses with a sour attitude, but that's something quite different from outright attacking people.
I do not believe in using a crop in order to get a result (when the horse doesn't do what I want it to do). There are better ways to train than with pain, and pain it is, when you use the crop any more than a very light flick.
BUT I sure believe that in the situations most of you describe here, if you come across a horse that wants to hurt you, you need to fight back as hard as you can, with whatever is at hand, and a crop is particularly useful since it can indeed inflict such pain. I would never punish such a horse for minutes though, or chasing it around whipping it, that IS cruelty. The horse does not know what it is getting hurt for, punishment is only effective if given promptly.
And the horse that wasn't put it its place and just acts careless, doesn't respect a human's space? Yes, one nice smack usually works wonders there as well. I agree it is better to put your point across firmly once, rather than being nice for too long and having a harder time getting rid of the behavior later on. However, it would be best not to let it come to that, when they start invading your space a firm word or hand sign is usually enough.
So, for actual disrespect and aggressive behavior, I would use a whip (I don't have one, only deal with my ow horses these days and they are friendly and sweet animals). For "correction" during riding or groundwork, no. But then I don't spank my children either, it's actually illegal in my country...