Of course, dogs, cats, steers, geldings and the other animals we neuter do it all the time. It has been done to men as well in history as a form of punishment or torture. And then of course women do quite well with out them ;)
There was a question about Hitler a couple of hours ago and you may not know that he had only one testicle. I don't think that's what killed him, though, but it might have been responsible for his Napoleon Syndrome.