A fine question. The short answer is, greatness.
The somewhat longer answer is, Shakespeare was successful in his own time, but not the near-god he is now. He was one of several high profile playwrights in his own time, but not the only one. However, with time most of his contemporaries faded into historical figures, while Shakespeare remained alive, with new generations finding new ways to relate to him.
The general reasons he's considered this great are the characters he created, and the amazing poetry contained in his plays. Figures like Hamlet, Othello, Iago, Falstaff, and others stay alive in the mind long after they've left the stage, and the lines from his plays… amazing.
If you're interested in a more detailed discussion of this, the April 2007 issue of Harper's magazine has an entire article on this process. (I'll include the link, but it's only available online to subscribers.)
And Shakespeare's not the only writer to attain this stature. Homer was more influential in classical Greece, and has stayed famous for thousands of years, compared to mere hundreds for Shakespeare.