Shakespeare's Richard III is a villain, I'm not disputing that. However, as with all of Shakespeare's villains, he isn't evil for evil's sake. We know why he feels such hatred - he's been treated like a freak his entire life. He's been hardened by the cruelty he's received and he's determined to make the world pay. He's full of bitterness. self-pity and jealousy:
"I, in this weak piping time of peace,
Have no delight to pass away the time,
Unless to spy my shadow in the sun
And descant on mine own deformity:
And therefore, since I cannot prove a lover,
To entertain these fair well-spoken days,
I am determined to prove a villain
And hate the idle pleasures of these days."
In a way, don't we feel sorry for him? Yes, he's malicious and unfeeling, but Shakespeare suggests that there is a human being beneath all that - a man who is acting out of emotions we're all prone to. Yes, he takes them to the extreme, but there still remains a sympathetic character underneath those violent, vicious acts. And, considering Elizabeth may not take too kindly to a 'human' representation of Richard, that's really quite dangerous territory for Shakespeare to be walking.
But, even if you disagree with that view of Shakespeare's Richard III, there is one more reason that I think the Platagenet king should be grateful to the Bard of Avon: there would not be half as much interest in King Richard if it weren't for his infamous status as Shakespeare's villain.
Realistically speaking, he should have no more than a brief footnote in history - a king (albeit the last in the Plantagenet line) who ruled for just a little over two years. Surely, the reason people all over the world are still fascinated by Richard and his legacy is not the facts, but literature. It's all thanks to Shakespeare.
So, whether Shakespeare got him all wrong or not (and that's a question we can still not fully answer) is perhaps irrelevant. He created a character that is bigger than the real Richard and given the 15th century king a level of fame he could not possibly have dreamed of. Some of that notoriety he might not be too thrilled about, but it's better to be remembered (even if it's for something that's not true) than to be forgotten, isn't it?