I have little tiny red dots all over my body. They look like moles what are they?

Red dots. I agree that they sound like cherry angiomas. However, an in-person medical evaluation can give you a certain answer.
Cherry angiomas. These are little collections of superficial capillaries. They are nothing to worry about. People get more of them as they age, some people have more than others. Wikipedia has a pretty good entry on them: http://en.Wikipedia.Org/wiki/cherry_hemangioma.