There are a bunch of theories. They are a kind of gentlemen-conspiracy theories. The phenomenon is basically founded in English class-snobbery: To some it is simply inconceivable that the son of a craftsman should be the greatest writer in the English language. So they concoct theories to prove the plays were actually written by some Lord or Earl or other person of better breeding and William Shakespeare, the commoner, was just a strawman or fake identity.
Oh, no, not that old chestnut: anyone who questions the Stratfordian theory is a snob and therefore wrong!
John Michell's book, "Who wrote Shakespeare?", is a great read: fun and informative. He doesn't argue for a particular answer to the question (which would have made the book much less fun), but the facts that he present do rather tend to support the idea that "Shakespeare" is likely to have been a closely-knit group of writers, with the actor from Avon being their front man and probably also a contributor, though we can hardly hope to ever know what exactly he contributed.
An interesting thing to ponder is why several fairly bad works were published under the "Shakespeare" name. Stratfordians say that those works weren't actually by Shakespeare (though if the contemporary attribution is not to be trusted why should we trust it in the case of the better works?) or that they were early works (even though some of them were first published later than the more famous ones).
It would be great if more people could accept the idea that several people can contribute to the writing of a play, just as several people can contribute to the writing of a novel (as in many well-known cases) or a film (as in almost every case).
It is actually quite interesting and fun to read up on.
But please do remember to apply Occam's razor liberally when researching. Fun and seductive as it might be to puzzle together a historical whodunnit from the lives of contemporaries and see if a theory can stick, there has never been a real reason to discard the notion that William Shakespeare was simply William Shakespeare. It is still by far the simplest answer that leaves the fewest gaps.