There are many fine authors from this period in addition to Shakespeare. One that immediately comes to mind is Christopher Marlowe, because he too wrote plays. However, Edmund Spenser also looms large, because his "Fairie Queene" was such a major play. (I also mention those two first because they show up in popular culture—Marlowe is in "Shakespeare in Love," for example.) One great thing about this period is that major historical figures also wrote: the explorer Sir Walter Raleigh, for example.
If you expand your focus beyond England, the pool of writers gets even richer: Machiavelli, Montaigne, More, and Cervantes are all Renaissance authors who are still influential today.