Greek Classics to read

Here's my list of the essential Greek Classics any college graduate should have read in Greek or a good translation.

Homer Odyssey Iliad
Hesiod Works and Days Theogony
A good anthology cover greek poets Trypanis perhaps
A good anthology with selection from most greek philosophers or a copy of Diogenes Laertius
Herodotus
Thucydides
Aeschylus' Persians the other plays if possible
Sophocles Theban plays but do try to read the others
Euripides one early one middle and of course the Bacchae
Aristophanes Frogs or Lysistrata at least
Lysias orations
Demosthenes
A general selection of other orators Classical and later
Plato The Apology Phaedrus Symposium As many of the others as you can
Aristotle The Nicomachean Ethics as for the rest oh dear which to choose
Rhetoric Poetics  Politics and his works on Logic!
Xenophon Anabasis
Polybius History
Do try to read one of the other hellenistic / roman greek historians
There's Appian Arrian Dio Cassius or Dionysios of Halicarnassus
Plutarch the Lives and try to read some of the Moralia too
The Greek Anthology
Apollonius Rhodios the Argonautica

Just read as much as you can