This is a great question that was asked of me by a friend who participates in my kickboxing class.
The answer is: yes, as long as the cheating day is in moderation.
(This answer, by the way, refers to dieting only.)
What if pizza is one of your favorite foods and you have deprived yourself of it until all you can think of is the gooey cheese and spicy sauce? By all means, indulge a little and give yourself the taste you crave. A slice or two for dinner will go a long way. It's eating the entire large pie that's not healthy.
People have a tendency to want things they can't have. Sticking to a diet is hard enough. Depriving yourself of some favorite foods for long periods of time you will make your miserable.
Be happy. Life is short. Eat healthy, eat smart and you can enjoy most of your favorite foods in moderation.