The ring of Gyges gave the power of invisibility to anyone who wore it. Simon confidently slipped the ring on and was thrilled at his disappearance. He enthusiastically walked around for a few hours testing out his new found "power". He was amused and excited at all the things he could do without being noticed. His mind slowly started tempting him to play innocent pranks on people. He tried to trip a few people, move a few objects around and laugh at the state of confusion etc. Soon his pranks seemed to be escalating and he had to stop himself and think about what he was doing. He was a little uncomfortable that he was drawn towards base temptations, such as peeking into private quarters. He tried hard to distract himself and concentrate on the good deeds he could do to put a smile on people's faces. But it was so very hard to come up with ideas for good deeds, when every second a silly prank sprang to his mind. He wasn't sure he could resist his temptations long. Would we have the strength to resist such temptations if we got hold of the ring? (Original Source: Book two of The Republic, by Plato)
This is a very interesting moral experiment. Often, conscience is attributed to our fear of being caught and punished. Many philosophers are skeptical that moral conscience can exist independent of fear of disapproval or punishment. It is an intriguing hypothesis to test with such a ring (or cloak) of invisibility. If one were invisible would their moral conscience remain the same? Probably not. It is easy to begin rationalizing every act as being harmless and innocent, although in the "visible" world we'll be stepping out of bounds of social convention and the dictates of moral behavior if we indulged in those acts. Eaves dropping, violation of privacy, purloining a few trinkets etc., will no longer seem as morally wrong, but mere privileges and harmless acts.
But it is not to say that the average person will drive himself to commit murder or rape. Or at least I can't imagine myself turning into such a person just because I have the power of invisibility. The assumption is that the core moral philosophy will remain same... or almost. Well, at least when circumstances are not too dire. I think it will be easier to convince ourselves of what is to be done when we encounter gray areas of moral dilemma, such as euthanasia. With no rules, restrictions or fear of punishments, it is easier to act on our impulsive decisions, for the consequences may not directly haunt us, beyond our conscience. It's a good personal test on our conscience. A person who finds himself drawing the line of morality quite differently from the way he currently identifies, will realize what his true underlying moral philosophy is, and where exactly his conscience stands in defining good versus bad. Anyone in a moral dilemma can imagine themselves executing an act when they are invisible and gauging how comfortable their conscience would be at that point. It will also help us isolate social conventions/restrictions from the true meaning of morality. Our underlying nature, personality and the values we truly believe in will come to surface.
It is also interesting that it's much harder to think of good deeds to perform when all that one can think of is suppressing base temptations, or yielding to silly, rationalized behavior to express freedom. But I will be optimistic - once we get over the urge to burst out and revel in our new-found precious freedom, I have hope that most of us will eventually consider doing "good" :)