So, to be able to say something about Richard III, that is, to be able to distinguish the real Richard III with Shakespeare's interpretation of the character, I've done a little research upon the matter. I believe that Shakepeare, although so great in his command of words, was not a historian. Therefore, his historical plays should not be entirely trusted as a guideline in any historical research.
Actually, prior to reading Richard III, some years ago, I read a few chapters of a book by Glenn Pierce, entitled King's Ransom in a library sort-of, but the book was gone when I came back some time later to continue my reading. In that book, Richard is described as a more modest and kind human being rather than a wicked ambitious demon. Thus these few last days I tried to find what other people say about Richard III.
Firstly, his looks. While Shakespeare described him as a hunchback, and practically a monster in appearance, such thing is not likely the case. In Richard's time, people who went to war needed to wear heavy armours and weapons. It is very unlikely that a man with hunchback could actually go to war, on a horse, and kill his opponents dexterously. The newly found remains believed to be the king shows that Richard III was not a hunchback, although he had scoliosis. It's in harmony with Rous and More's report that one of the king's shoulder is higher than the other. 
|The newly-found Richard III remains|
Now, about the murders that Richard III committed in Shakespeare's story. Scholars are still debating whether Richard really committed all of those murders. It's actually interesting to read what the Richard III Society has to say about it. It's not so much to conclude that Shakespeare's description of the king's homicidal character is too much dramatisation with less historical accuracy.
On the contrary, many people in Richard's era described him as a brave soldier, a good member of the family and also a good king. Instead of being a tyrant, he encouraged justice in all his region.
Why, then, did Shakespeare write such a play, and how could such a play labelled as 'historical'?
Shakespeare complied with the general belief of his era that deformity in flesh reflects the deformity in moral qualities as well. Moreover, Shakespeare lived under the reign of a Tudor sovereign, thus it would be easier for him to glorify the present dynasty rather than to give balanced view of the former one.
Another reason. There are writings available in Shakespeare's era which might be biased and not credible. Among those are writings by Polydore Vergil and Sir Thomas More. Shakespeare was also believed to have taken his history from the Chronicles, which quality is varied when it comes to accuracy. 
Whether Richard to some extent had really been a bad tyrant, or whether he had been most unjustly accused of committing terrible things he had never done, most of us would agree that Shakespeare's play Richard III remains a masterpiece – even those supporting Richard wouldn't deny that. But this play reminds us all that we have to carefully choose between fact and fiction and make sure of everything before believing it entirely.
That's all I think. I am no expert in this matter, I'm sorry, but it has been fun to dig deeper into history this time. I encourage you all to read these links below, in order to see Richard III from another point of view.
Richard III Society. http://www.richardiii.net/2_5_0_riii_controversy.php#crimes
Richard III Society. http://www.richardiii.net/2_3_0_riii_leadership.php#parliament