Richard III
The real Richard III only partially resembled the scheming lump of deformity depicted by Tudor historians and Shakespeare. Richard, Duke of Gloucester, was the younger of Edward IV's two surviving brothers and the only one whose loyalty was steadfast--one of several things contrary to Shakespeare's portrayal of him.
Richard's elder brother George, Duke of Clarence, was a more blatant schemer; his incessant plots to further his own power ended with his execution by Edward IV (by drowning in a butt of malmsey wine).
On Edward IV's death, Richard was readily accepted by the Great Council as Protector of Edward's two young sons, probably in accordance with the late king's will.
A coup d'état
The reasons behind Richard's ambitions seem to have been practical rather than merely greedy, but he was as guilty of ruthlessness as many princes before and after him. Chiefly supported by the Duke of Buckingham, Richard carried out a coup d'état, eliminating or arresting potential opposition and imprisoning the two princes in the Tower of London (where they were probably murdered under his orders--thought there is no direct proof).
Richard used the familiar claims of usurpers to justify his actions: that those he deposed were illegitimate and that he himself would bring a better order. But he also followed through with his promises, prohibiting forced monetary "gifts" to the crown, and making improvements to the legal system (mainly concerning property rights and court procedure*); the Parliament of 1484 therefore confirmed his reign willingly.
(The quotations from Holinshed are taken from the edition by Hosley; Polydore Vergil and the York Records are quoted in Cook, Lancastrians and Yorkists: The Wars of the Roses.)
Historical documents on Richard III can be accessed through the Richard III Society.
Footnotes
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Improvements to the system
For instance, the requirements for jury service became more discriminating and a defendant's goods were protected against seizure while he or she was in custody.