OK, firstly a list of what I'd regard as the 'fundamentals'. This doesn't necessarily include my favourite bits of writing. Rather, it's a list of 'canonical' literature which would usefully inform any reading of later work. (some will overlap with what people have said already). I'll leave it to someone else to fill in post-Milton.
Homer: The Illiad, The Odyssey
Aeschylus: The Oresteia
Sophocles: Antigone, Oedipus Tyrannus, Oedipus at Colonnus
Euripides: Medea, Electra
Virgil: The Aeneid
Ovid: Metamorphoses
The Bible - at the very least the first five books, the Gospels, and Revelations, though it all helps.
Chaucer: The Canterbury Tales
Shakespeare: read according to your own preference.
Milton: Paradise Lost
And, since this is the area I've specialised in, my must-reads for Elizabethan / Jacobean Drama. (Again, deliberately a non-obscure list, though I'm happy to suggest some more off-the-track stuff if anyone wants.)
Kyd - The Spanish Tragedy
Marlowe - everything really; it's all stunnning. Tamburlaine and Faustus are the most central. Read both texts of Faustus.
Beaumont - The Knight of the Burning Pestle (there's nothing else quite like it; I think it's hilarious)
Middleton - The Revenger's Tragedy, Women Beware Women, A Game at Chess (possibly my favourite playwright from this era)
Webster - The White Devil, The Duchess of Malfi
Jonson - Volpone, The Alchemist (I've never really got along with Jonson, but he is important to the whole scene)
Some theory:
Auerbach - Mimesis (A mind-blowing account of representations of reality in Western Literature from Homer to Woolf. You'll never read novels in quite the same way again.)
On a slightly less esoteric note, Peter Barry's 'Beginning Theory' is an excellent and reasonably comprehensive introduction. The OUP Very Short Introductions are also great - the Postmodernism and Postcolonialism ones are very lucid and readable.
And, lastly, an honorable mention for Laurence Sterne's Tristram Shandy - a novel (apparently) that's at least 200 years ahead of itself.