Not being any kind of scholar, I've only read Greek works if they're available in cheap, translated form, but I've read a good percentage of those. I love the
Iliad. It's probably a bad translation, but my go-to version is Ennis Rees' verse because of its speed and vigor - it really moves. Though I do also like the Lang/Leaf/Myers prose of both the
Iliad and
Odyssey with its King Jamesish grandeur. I'm not as big a fan of the
Odyssey, but still like it (Robert Fitzgerald's verse there).
Euripides is the rare Greek I don't really like. I love Aeschylus and Sophocles, though. Only seven plays left of each (plus fragments and a satyr play (unless they've changed the attribution)) so there's little point in picking out any vs. reading them all. And Aristophanes has about eleven surviving works and has been funny for over two thousand years.
Speaking of fragments, that's all Sappho is, but she's worth seeking out individually. I like Mary Bernard's rendition which I have in this tiny Shambala edition. She and Pindar (one of Lattimore's several) are the only writers of shorter poems I have outside of anthologies. For other, longer poems, Apollonius' work on the Argo is of course not comparable to Homer, but still fun. (And it's about the Greek "hero" Jason!
)
Oh, and I'd completely forgotten Hesiod (Thanks, KGeo777). Also not the biggest fan, but
Theogony is interesting. It and
Works and Days are more interesting for myth and sort of history/sociology than poetry, though, to me. Kind of like the Hippocratic writings - not a lot of fun as such, but they shed a lot of light on the day-to-day of the era. Plus, with those: early science! And then I'd also forgotten to mention the
Homeric Hymns. Kind of part-Homeric, part-
Theogony, part-Pindar.
Plato is the other giant Greek I don't care for, though it's hard to ignore his influence or Jowett's prose. I haven't gotten into the more complicated, abstruse Aristotle for the most part, but I love his more "humanist" works of the
Nichomachean Ethics,
Politics,
Rhetoric, and
Poetics. The first and last of these, especially, are among the greatest on their subjects of all time. The Ross set has essentially everything.
For history, I've read a few translations for a few works but, based on just
The Landmark Thucydides, I enthusiastically recommend the Landmark series. (I bought the
Herodotus,
Xenophon's Hellenika, and
Arrian's The Campaigns of Alexander on the strength of it. Herodotus is a blast and Arrian is the best ancient work on Alexander - oddly, I haven't read any Xenophon yet, though.) Plutarch also did philosophy and odds and ends, but his
Lives are the most famous, and essential. The lives were written in pairs with comparisons but I read the Penguin versions which didn't include all of them, separated them, arranged them in chronological order, and ditched the comparisons - so I look forward to reading the whole surviving corpus properly arranged someday. (I have the "Dryden" translations for that.)
One of the oldest books I have is a 1900 copy of a bunch of orations of Demosthenes (plus three others by three other orators - Pericles (perhaps actually Thucydides rendition of what Pericles might have said), Aeschines, and Isocrates) which has a companion volume of Cicero (with a Caesar and a Cato). Especially given the translation, I have them more for history than oratory, but they're interesting.
Then there are odds and ends which I have but haven't read like Pausanius'
Guide to Greece and Apollodorus'
Library. Plus, all this and more can be found online if you don't mind older translations and scholarship. But if it was good enough for Bury, Kitto, Finley, Tarn, et al., it should be okay for anyone. (And Durant - this is mostly Durant's fault because his
Story of Civilization and a copy of three random plays edited or translated by Blanche Yurka that I'd randomly run into earlier kind of made me want to dig deeper and it ended up being a kind of passion.)
By the way, if anyone knows of a book on the great English classical scholars and historians of Enlightenment-WWII era, I'd love to know about it. Seems like there has to be such a thing but I've looked and can't find it.