On this the anniversary of his death, I went hunting for references to Shakespeare and Stanley Kubrick. What I found was a quote from the man himself (Kubrick that is - Shakespeare was relatively silent on his impressions of Stanley):
How do you explain the kind of fascination that Alex exercises on the audience?
I think that it's probably because we can identify with Alex on the unconscious level. The psychiatrists tell us the unconscious has no conscience -- and perhaps in our unconscious we are all potential Alexes. It may be that only as a result of morality, the law and sometimes our own innate character that we do not become like him. Perhaps this makes some people feel uncomfortable and partly explains some of the controversy which has arisen over the film. Perhaps they are unable to accept this view of human nature. But I think you find much the same psychological phenomena at work in Shakespeare's Richard III. You should feel nothing but dislike towards Richard, and yet when the role is well played, with a bit of humour and charm, you find yourself gradually making a similar kind of identification with him. Not because you sympathize with Richard's ambition or his actions, or that you like him or think people should behave like him but, as you watch the play, because he gradually works himself into your unconscious, and recognition occurs in the recesses of the mind. At the same time, I don't believe anyone leaves the theatre thinking Richard III or Alex are the sort of people one admires and would wish to be like.
Emphasis mine. If you don't recognize the context, they are speaking of the lead character in A Clockwork Orange.
Full interview (or, at least, the public excerpts) available here.