I would have to go with
lordhelmet's second choice: Muhammad. I can think of no other leader who has had as profound an impact in the religious sphere, the political sphere,
and the military sphere during his lifetime - and major geopolitical ramifications ever since.
I can't really count Jesus (indeed, I would probably put Paul ahead of him in a ranking). After all, the mission of Jesus was an abject failure - maybe one in a hundred of those identifying themselves as followers of his teachings even know what his teachings were - and
maybe one in a thousand of them who actually
follow his teachings. It was Paul who turned a minor Jewish cult into a religion with a broader appeal, largely through bastardizing the intent of Christ, adding a lot of popular prejudices (mostly his own), and coopting rites from several competing religions. Jesus himself was a fairly minor - and still largely disregarded - figure in the general scheme of things.
I would be equally dubious of Copernicus as having had much impact in reviving the heliocentric notion of the universe that had been put forward by Aristarchus, Hermes Trismegistus, and Aryabhata. Further, his
De Revolutionibus was published immediately before his death, was dedicated to Pope Paul III, and was well-received by many in the Church (with the exception of the Dominicans), so his theory was hardly "dangerous for himself" nor for the views of the Church. Indeed, the first person to raise any sort of alarm about Copernicus was Martin Luther. It wasn't for another fifty years that, under the influence of the Dominicans, the Ptolemaic system became the "authorized" theory. It was Galileo who was eventually put under house arrest for expanding on the heliocentric theory, contrary to the ambitions of Cardinal Bellarmine - and
he recanted.
Copernicus, by the way, was quite
wrong. He believed that the Sun was the center of the universe and that
everything revolved around it - including all of the other stars. If anyone comes close to single-handedly changing the way we perceive the world, it would have to be Johannes Kepler, who vastly improved on Copernicus' faulty speculations.
Erasmus would maybe be a contender (I'm astonished that
anyone has never heard of him

), but, like Jesus himself, his opposition to formalism (respect for dogma without consideration for the actual teachings of Christ) has proved to be a failed mission. His greater influence was probably in his popularization of texts by Aristotle, St. Augustine, Cicero, St. John Chrysostom, and dozens of others through his prolific translation and publication of their work.
Shakespeare? As one of the first and most popular of the pre-Enlightenment humanists - and as a dramatist - he has had some influence. But in terms of revolutionizing "the way theaters are run and how shows are put on", I'm afraid he can't be given much credit. The Elizabethan theatre system was well in place by the time Shakespeare came on the scene and, while that tradition may have influenced some nineteenth century actor-managers, it has hardly had a lasting impact. As to "how shows are put on", apart from giving characters considerably more motivation and depth, there's little evidence that Shakespeare himself would have had much impact at all on staging. If there
was much innovation, it was more likely due to the efforts of Richard Burbage.
Nah, I'm going to have to go with the consummate secular leader, the effective preacher, the outstanding and humane military strategist, the unifier of Arabia, the founder of a powerful dynasty (or two), the Prophet of Islam, Muhammad.