Yes it does work. A friend of mine qualified as a hypnotherapist.
I've never been sure about stage acts though, but there does seem evidence and anecdotes that suggest it's real. I'm not a very good subject for hypnosis, my mind doesn't switch off very easily!
All it is , is putting suggestions into the sub-concious mind. It can be used to cure phobias, addictions, etc. I'm not saying it always works, but there are some success stories.
Knowing how it's done, years ago I did a little experiment on a couple of friends. One was totally amazed that I made his fingers or arm move without him making any conscious effort of thought to do it. Again, it was just suggestion.
I imagine it can be dangerous if not used correctly. For example, if you leave the suggestion that there is a mad dog in the room and you don't take that thought out of their mind before waking them they could develope a fear of dogs.