Ancient Classics

Homer - Iliad, Odyssey
The national books of the Greeks. 

Aeschylus - Oresteia cycle: Agamemnon, The Libation-Bearers, The Eumenides
A cycle of 3 plays, mainly about Orestes, the son of Agamemnon.  In the first is the story of Agamemnon's murder by a conspiracy including his own wife, who is angry at his having sacrificed their daughter, Iphigenia, in order to get safe passage to Troy.  The second is Orestes revenge.  In the third, Orestes v. Furies are put on trial before a jury of Athenians.

Sophocles - Oedipus cycle: Oedipus Rex, Oedipus at Colonus, Antigone
An even more famous cycle of 3 plays, mainly about King Oedipus of Thebes and, well, I don't want to give away the tragic plot, but as tragic drama it ranks right up there with Shakespeare's "Romeo and Juliet" and Goethe's "Faust".  This is also where we get the term Oedipus Complex from.

Herodotus - Histories (an account of the Persian wars)
The Greeks are a young group of waring city states, who unfortunately manage to anger the Persian emperor.  So what do you do against an army of a million men who can build a mile-long bridge to cross the Hellespont from Asia to Europe?  First you stop fighting each other, and second, you send an army of 300 Spartans to deal with the Persians.  They even made a movie about this a year or so ago, which my friends who watch R-rated movies tell me is totally awesome.

Thucydides - History of the Peloponnesian War
Xenophon - Hellenica (end of the Peloponnesian War)
The two greatest city-states in Greece were Athens and Sparta.  This is the story of their prolonged war for dominance, which occurs during (and ends) the Golden Age of Athens.

Plutarch - Lives (of the Noble Greeks and Romans)

Plato - Republic; Euthyphro, Apology, Crito, and Phaedo

Aristotle - Poetics, Nicomachean Ethics, Politics
No philosopher has been more highly regarded for a longer time than Aristotle.  His words where practically considered gospel by the middle age catholic church, much to the consternation of those who later tried to correct a few of his errors.  Find out what it's all about, because I'll probably assign readings from these works anyway.

Arrian - Anabasis Alexandri (together with Plutarch's Life of Alexander)
Philip II of Macedon was one of the world's greatest kings and generals.  Unfortunately, he is mostly forgotten and completely overshadowed by his son, Alexander the Great.  He solved the Gordian Knot, and conquered the known world, at least until his soldiers finally got tired of victories at the border of India, and said they wanted to go home finally.

Virgil - Aeneid, Georgics, Eclogues
Why do people from George Wythe refer to agriculture as "Georgics"? Because of Virgil! The 17th century poet John Dryden described The Georgics as, "The greatest poem by the greatest poet."

Livy - Early History of Rome
Thomas Jefferson wrote to his nephew that there were three books every gentleman had to have familiarity with; Plutarch's "Lives", Livy's "History of Rome" and Virgil's Aeneid.  It's massive even though most of it has been lost, so consider limiting yourself to the first 5 books, which covers about 300 years starting with the founding, and includes the famous story of the Sabine women, which I should tell in class sometime.

Cicero - De Officiis, Orations (Against Verry, Against Antony), Essays (On Old Age, On Friendship), The Republic, The Laws
De Officiis (On Moral Duties) is especially recommended, written in the last year of Cicero's life to his son at Univerity in Athens, it expounds his thoughts on the best way to live.

Tacitus - Annals (Rome from Augustus through Nero)

Suetonius - Lives of the Twelve Caesars (Julius through Domitian)

Lucretius - On the Nature of Things
(A Science classic!) "According to Lucretius's frequent statements in his poem, the main purpose of the work was to free Gaius Memmius's (and presumably all of mankind's) mind of superstition and the fear of death. He attempts this by expounding the philosophical system of Epicurus, whom Lucretius apotheosizes as the hero of his epic poem." --wikipedia

Josephus - Wars of the Jews
A first-hand history of the Jews from the time of Herod until Jerusalem is sacked by Vespasian and Titus.

Julius Caesar - Commentaries, Gallic Wars
Caesar is not only a great general and ruler, he's a great orator too.  One of the greatest and most famous speeches in history is only three words long!

Xenophon - Anabasis
An adventure of Greeks into Persian territory and the long, long road home. 

Hamilton - Mythology
I read this when I was very young, and thought mythology was the most exciting thing ever for years.  Here you can find out what Shakespeare is talking about half the time, because these stories are the archetypes for all of western drama.

(Other modern classics, such as Augustus Caesar's World may also be acceptable choices.)

Euclid - Elements
Still sets the standard for teaching geometry. 

Nichomachus - Introduction to Arithmetic
This is nothing like Euclid, thank goodness!  It's much much shorter and much much easier to read, and still considered a math classic.

Polybius - Histories (220-167BC - Rome becoming a world power)
This history covers a pivotal time in Rome's history, as it grow from a city state into a world power.  It includes the war against Hannibal, who brought elephants from Africa via Spain over the Pyrenees mountains into Italy, completely defeated the Roman armies three times, and even threw a spear over the wall into Rome itself, but never quite manages to win the war.

Marcus Aurelius - Meditations
Personal thoughts from a Roman Emporer at the height of Roman power. Read and compare it with Ecclesiastes for more insights. 

Sun-Tzu, The Art of War
War isn't all glory and battles.  It's hard work and difficult management, which are skills applicable to everyone's lives.  This may be the world's first managers' self-help book. 

Aesop, Fables

(pseudo-)Apollodorus - Libraries
One of the primary sources of the mythology of the Greek gods and heros.

Web Resources

Perseus Digital Library: http://www.perseus.tufts.edu/hopper/

The Internet Classics Archive: http://classics.mit.edu/

Internet Ancient History Sourcebook: http://www.fordham.edu/halsall/ancient/asbook.html

The Theoi Classical E-Texts Library: http://www.library.theoi.com/

Also:

Project Gutenberg: http://www.gutenberg.org/

Google Books: http://books.google.com/

Forgotten Books: http://www.forgottenbooks.org/

Squashed Philosophers (condensed versions of some important philosophical books): http://www.btinternet.com/~glynhughes/squashed/index.htm