Based on my limited and amateur knowledge of the subject, many people believe Richard III murdered the Princes in the Tower. I'm curious as to why the debate over the innocence of Richard III seems to have attracted so much interest, especially in non-academic circles (even before the rediscovery of his remains in 2012). Why does the Richard III society exist? Why do so many portrayals of him in popular culture (such as the Phillipa Gregory "Cousin's War" novels and associated TV shows or the historical novel The Sunne in Splendour) exonerate him or portray him in a positive light? Or, in other words, what is it about Richard III that makes people so willing to defend him 500 years later?
Without getting into the "did he do it" debate, I think part of the reason this historical mystery is so divisive is that much of Richard III's popular posthumous image is the result of Tudor propaganda or the Shakespearean portrayal. Henry VII had a pretty weak claim to the throne, and took any opportunity he could to paint himself as the rightful heir to the Lancastrian dynasty.
After his win at Bosworth, Henry took every opportunity to paint Richard as a usurper. In parliamentary records, he dates his reign prior to Bosworth, refers to Richard as the Duke of Gloucester, and calls him not the rightful king. There was an ever present threat that another Yorkist (be it Perkin Warbeck or a de la Pole) would usurp the crown, and propaganda was an important weapon in preventing this.
The narrative that the Tudors created was picked up by Shakespeare:
Above the hubbub of a late-Elizabethan theater, the nuances of political history could be lost. But the mere sight of actors dressed as aristocrats, teaming off according to their choice of rose, was designed to be instantly understood. Henry VI, Part 1 eventually became part of the cycle of Shakespeare’s two historical tetralogies: eight plays that run, if arranged according to their historical chronology, from Richard II to Richard III, and which portray the whole course of pre-Tudor fifteenth-century history. The message that had been concocted by Henry VII nearly one hundred years previously had become entrenched in public consciousness. And there it has remained, more or less, ever since (Jones, 332).
It seems as though the attempt to salvage his historical memory is a fairly recent development, emerging in the 20th century.
The Richard III Society was founded in 1924 by a group of "enthusiastic amateur historians with a particular interest in the life and times of Richard III". According to the society, they believed that history had painted in an un-fairly negative light.
The modern pro-Ricardian movement, if you can call it that, was bolstered by the publication of popular books such as Dickon by Marjorie Bowen (1929) and The Daughter of Time by Josephine Tey (1951). These books were both works of fiction, easily accessible to the general public. In Daughter of Time, Tey tells a compelling story of a detective set on discovering the truth behind Richard's historical persona. It reads as a mystery, slowly revealing evidence suggesting that Richard might not be the villain history has remembered him as. The book is often considered a classic mystery novel, and its popularity helped pro-Ricardian ideas become more widespread.
Jones, Dan. The Wars of the Roses: The Fall of the Plantagenets and the Rise of the Tudors (p. 332).
Tey, Josephine. The Daughter of Time.