Most cultures and societies have a period in their histories in which they are conquered and/or enslaved by someone else.

I don't think I'd agree with that at all actually. Racial slavery is a very new thing, and mass slavery according to cultural lines simply did not happen in antiquity. War captives certainly exist in large numbers, but it's not as though the mass enslavement of one city means the mass enslavement of culturally similar cities nearby that may or may not be politically related--the slaughter of the Plataeans by the Spartans did not mean the slaughter of the Spartans' Boeotian allies, and despite Caesar's enslavement of the enormous number of captives he took in Gaul the vast majority of people living in the area for the next couple hundred years would still be Gauls.

Greeks were enslaved literally all the time, generally by other Greeks. The constant inter-city warfare of the Greek world led to no shortage of captives, and the threat of enslavement through piracy was an ever-present concern to ancient travelers--a common theme of New Comedy was the revelation that the slave girl with whom the protagonist has fallen in love is actually the daughter of some incredibly important person who was captured by pirates when she was young and sold into slavery. At Athens most slaves were either Thracians or from the Black Sea area, followed by other Greeks--one's slave might look identical to his master, he might speak the same language (even the same dialect!). Later, Greek slaves became a favorite of wealthy Romans as house slaves, for their pedagogical skills and the cultural value of their existence as Greek-speakers in general (a category which had greatly expanded by the time the Romans got their to include many peoples who were not ethnic Greeks--to a Roman "Greek" encompassed Syrians and Hellenized Egyptians as well as Greek mainlanders). The slave trade in the Roman eastern Mediterranean, dominated by pirates and centered on the free port at Delos, was simply enormous, and even with the pacification of the area and the destruction of the pirate fleets the eastern slave trade persisted as a large-scale industry throughout the Republic and the Principate