Luis Vas de Camoes (1524-1580)
Lusiad (Os Lusiadas) (1572), Portuguese.
The Lusiad describes Vasco da Gama's voyage all the way round Africa to India, which was pretty clever, at least until they invented the Suez Canal. Highly rated if you can read Portuguese, but since that means you probably are Portuguese, or at least Brazilian, we won't trust your judgement on grounds of bias.

Ariosto Ludovico (1474-1533)
Orlando Furioso (1532), Italian.
Orlando Furioso is highly rated, about the crazy adventures during the crusades of mad Orlando. It also features someone riding a hippogriff to the moon, a hippogriff being 1/4 lion, 1/4 eagle and 1/2 horse, but not having any cow in the mix, it didn't jump over said lunar object.

John Milton (1608-1674)
Paradise Lost (1674), English.
Paradise Lost contains some of the greatest poetry in the English language, but is by and large totally unreadable. This is despite being one of the few epic poems based on a story anyone has ever heard, the early part of Genesis. Milton was blind, long-winded and a puritan, but also a campaigner for a free press (about which he wrote Areopagitica, possibly the best ever title for a pamphlet in defence of a free press, named for the hill where the Athenian Supreme Court met, Areopagos). Milton is most famous for being, according to William Blake, a satanist and thus a poet*.

Torquato Tasso (1544-1595)
Rinaldo (1562), Gerusalemme liberata (1575), Italian.
Alliterative names are always cool, and he sounds sort of like Torquemada, boss of the Spanish Inquisition. On the negative side, he was a big influence on Edmund Spenser. Also big on crusades.

Edmund Spenser (1552?-1599)
The Faerie Queene (1596), English.
In the entire 5 million years since our ancestors climbed down from the trees no one has ever read The Faerie Queene, not even Spenser, who left it unfinished. It is believed to be an epic poem about the wonderfulness of Queen Elizabeth I, the Virgin Queen (although it is not intended as a slight on her sexuality, the epithet "faerie" referring only to male homosexuals). It is written in stanzas of 9 lines, about 8 more than most readers can manage.

Virgil (Publius Vergilius Maro) (70 BC-19 BC)
Aeneid (19 BC), Roman, wrote in Latin.
Not a Renaissance poet, but the poet every Renaissance epic poet wanted to be. He set an excellent precedent by demanding his relatives destroy his epic poem about the founding of Rome. However, they in turn set a different kind of precedent by refusing his wishes.

*Not strictly true. "The reason Milton wrote in fetters when he wrote of Angels and God, and at liberty when of Devils and Hell, is because he was a true Poet, and of the Devil's party without knowing it." The Marriage of Heaven and Hell, William Blake (admittedly words spoken by Satan, whose impartiality is in doubt).