One thing that really intrigued me about this play was just how bloody Richard's hands were. He would stoop at nothing to gain his ends. I wondered if that was really the case, or if Shakespeare dramatized his morally repugnant character to become larger than life.
I thought I would look into this a little deeper, to see what the truth might be. So far, the Britannia Encyclopedia said that the evidence for Richard's murders of his brothers and nephews was "based on purely circumstantial evidence."
I also read up a little in a book called History of the Life and Reign of Richard the Third. In my opinion the book is pretty biased, but it gives a much kinder representation of Richard than Shakespeare. Some of the evidence it gives to disassociate Richard from the young Prince Edward's death is the location of Richard in northern England at the time, as well as Richard's pledge of support to the young prince.
Honestly, either way you put it, he probably was responsible for some of the ill that happened during his reign. He definitely stood in the position of the most benefit for the majority of the murders.
However, I think it's important to note that, through no fault of his own, Richard III's rule served to help reunite England.