Mary I & England's Catholicism
Another possibility would be with Mary I. Although popular opinion holds that she was the hated "Bloody Mary," she actually wasn't that unpopular of a monarch, and had she lived a long life and been a bit more flexible, she could have "reconverted" the island.
Let's assume she doesn't die in 1558 and lives a long life as queen, with or without an heir. What made Elizabeth a good queen was her ability to accommodate a large variety of people. She wasn't a hardcore Reformer; she was actually quite conservative, and she was more interested in the appearance of conformity and social peace than making sure people really "believed" in Protestantism. Had Mary been more like that, she could have, over a long reign, been effective at reuniting England with Rome. Her issue, though, was she was more devoted to her religion than to her country, so she ended up making more problems for herself than she needed. But, Catholicism itself was still pretty widespread. Especially in the countryside, many people were not too hot on the Reformation; a lot of churches that had been ordered to destroy icons during Edward VI's reign had actually only hidden them, and brought them out when Mary took office. Her main problem will be dealing with the merchant class and those people who got lands from the dissolution of the monasteries.
So let's assume she does a few things:
1) She allows the Bible to be translated into English.
2) The Anglican service is pretty conservative, but she institutes a more formal Mass in English, retaining more of the Roman practices.
3) She reaffirms her devotion to the Pope on spiritual matters, but asserts her power as supreme governor of the English people. Such a move would essentially maintain Henry VIII's separation from Rome, but would at least seem to play ball with the Vatican, which would perhaps be all they need.
4) She purges the clergy both of the corrupt (pluralists and absentee priests) and of hardcore reformers. She takes their land and turns part of it over to the various monastic orders that had been dissolved.
5) She allows moderate reformers to remain, but forces them to acknowledge the spiritual authority of the Pope (as well as her authority as ruler of England).
6) She institutes certain protestant-minded reforms (bans the sale of indulgences, etc, but affirms priestly celibacy).
7) She demands conformity (a la Elizabeth) in practice, but like her sister, does not wish to look into the souls of men.
I think this would end up creating a Catholic-lite England, slightly more Romish than the Anglican church, but still nominally affiliated with the Vatican.
Short-term & long-term effects:
1) Shakespeare. There was already a strong theatrical tradition in England (mystery plays and such), so there's no reason to assume a Catholic England would not retain it. The main issue, though, is what the nature of the public theatre would have been. Assuming the man we know as Shakespeare was still born, he could have gone into the theatre. Although, would he have been able to so easily leave his wife behind in Stratford to go to London? Who knows.
2) The effect would be much stronger on later poets. John Donne and George Herbert, for example, assuming they still exist, would be very different writers. And John Milton would probably not exist.
3) The new world: a joint Spanish-English production? There would probably still be colonies consisting of Protestants, but they'd probably be less exclusively of the Puritan bent. No reason to assume that there wouldn't eventually be a rebellion, although its outcome is hazy...