Livy, writing about the founding of Rome over 500 years after it happened, Plutarch writing Lives of people long dead, Herodotus writing about long ago migrations or events...
What kind of evidence (now probably lost) would these historians have had access to? Were there histories of these events that later historians based their work off of? What were these like? Are these reliable? And how much of their evidence is simply oral tradition?
Tagging on, I'd like to know how important the Library of Alexandria was to historical documentation.
Some of Herodotus's sources came from oral traditions and word-of-mouth that he gathered in his travels. I'm not sure to what extent, really. I do know, though, that there were some interesting mistranslations between the source and what Herodotus ultimately penned, the most infamous of which being the giant, gold-digging ants that supposedly lived in India. There have been speculations on what the animal could have been -- marmots being the one that I hear about most commonly -- but I'm not sure how speculative that is.
I know that the ancient Mesopotamians (sorry not aware of which ones) were able to copy down history.