When I was teaching at the University of Georgia, one of my favorite tidbits to drop in the middle of Hamlet or Macbeth was the fact that there is no original Shakespeare.
Shakespeare himself did not publish his plays, because copyright law as we know it did not approach existence until 1710. The nineteen plays that were published during his lifetime were most probably not approved or overseen by him. The rest were published seven or more years after his death, and probably not from a written script, but from the memories of his actors.
Memory is a funny thing. There are actually two equally authoritative and mutually incompatible versions of King Lear. No one knows which one is the "real" one. Perhaps they both are; Shakespeare doesn't strike me as someone who would be afraid of a little retconning. Aside from protecting his intellectual property by the only means available, one reason why Shakespeare might not have wanted his plays in print is that then he'd be bound to that version. I'm just speculating, but he loved topical jokes and those often have an expiration date. Of course his other favorite, dick jokes, spring eternal.
Shakespeare introduced and possibly invented out of his own noggin something like 1700 words, and his turns of phrase are so common as to be found absolutely everywhere, from William Faulkner to Monty Python. He is probably the single most culturally significant writer in the English language. Yet we don't have his original, physical words at all.
The ambiguity and the lack of actual pages with his writing on them are also why there are so many theories about his work being written by someone else. I think he probably did collaborate on some things and he absolutely, definitely, without a doubt stole whatever wasn't nailed down hard enough. But there's no accepted body of evidence that any other person wrote what is attributed to him, certainly not that any one person did so. However, his looming presence in the culture means that the aura of mystery is attractive to the sort of person who wants to believe that the world as we know it is a tissue of lies and they are on the heels of the real truth.
Furthermore, Shakespeare has the colossal influence that he does partially because Victorian literary critics decided that he should. They lifted him up as the greatest writer of all time, and he therefore became almost universally read by anyone who could read English, to the point where if you made an allusion to or quoted him you could be sure that the reference would be understood, and then it just snowballed. At this point if you want to understand English literature you have to know Shakespeare. He is absolutely, aside from the merits of his actual writing, a kind of ur-example of hype...a situation he would probably find gratifying and hilarious. No one who loved a pun so much at that man did could fail to be amused by irony. And no one who could write Hamlet...a play that is very much about layers of perception, deception, delusion, and the possibly empty reality underneath...could fail to apprehend the irony of his own literary ghost.