My interest is a little incongruous, since I am by no means a Shakespearean. I am, however, conspiracy minded.
There's a movie about the Authorship Question due out soon, called Anonymous. I just heard about it the other day, and it sounds like a far cry from Shakespeare In Love. According to some stuff I found on the Internet, Anonymous "speculates on an issue that has for centuries intrigued academics and brilliant minds ranging from Mark Twain and Charles Dickens to Henry James and Sigmund Freud, namely: who was the author of the plays credited to William Shakespeare?"
When you really delve into the Authorship Question, aka the Authorship Controversy, it's a complex issue. But at its heart is the simple discrepancy between the established facts of the life of "William Shakepere" and the nature of Shakespeare's works. The known Shakespere seems to have been an uneducated rustic, an illiterate boob. Yet the plays and sonnets are the most exalted works of Western literature.
I can't remember now when I first heard about the Authorship Question. But my interest wasn't very strong until I saw a PBS Frontline episode about it. It centered on Edward de Vere (above), the Seventeenth Earl of Oxford. Many believe de Vere is the true author of at least some of the Shakespeare canon, in particular the Sonnets, and perhaps Hamlet.
The value (and ultimate message) of Anonymous remains to be seen. Will it straddle the fence? Will it champion de Vere as the true author of Shakespeare? Or another candidate, such as Francis Bacon, or Christopher Marlowe?
You can find a good overview in a book called Who Wrote Shakespeare? by John Michell. The case for de Vere is fully explored in The Mysterious William Shakespeare, by Charlton Ogburn, Jr.
Or, you can read this entry in good ol' Wikipedia.