Does your cat hunt - and how do you deal with it?

I know some people keep their cat as a purely indoors pet and so those should (hopefully) not be presented with the chance to hunt anything other than an occasional spider, but what about the cats that go outside?

Obviously hunting is a totally natural drive in cats and if they see possible prey they are going to instinctively try to catch it and should never be punished. On the other hand a cats natural behaviour can seem cruel to us especially when they don't kill straight away.

Does your cat hunt? Do they present you with dead things? Or do they bring live prey home and continue to play with it? How do you handle it? Do you wish you could stop it?