This isn't an easy question to answer, because Greece and Rome were both very different from one another and were home to a variety of different cultures and sexual norms in themselves (Sparta was different from Athens, the City of Rome different from many of its states). It's also difficult to know what an 'average' person would be into.

That said, sexuality certainly seems to have had different meaning in the ancient world. Ancient literature and images seem to portray a world in which a married man could sleep with his wife, prostitutes, mistresses, slaves and young boys, without facing much moral judgement. Lots of current scholarship debates why this is. It seems likely, though, that in a world without a religious dogma that praised chastity and marriage over sexual desire, sexuality was not such a morally charged issue as it is in much of the modern world. Hence it wasn't categorised or classified in the same way, because if you had the money and the power you could kind of do what/whoever you wanted.

It's worth noting that the same does not appear to be true of women, presumably because of the need for clear bloodlines.

It's a complicated and much-discussed subject in modern scholarship, with interpretations heavily influenced by the culture and perspective of the author.

Good sources on this stuff: Plato's 'Lysis' and 'Symposium'; Keuls's 'Reign of the Phallus', Kiefer's 'Sexual Life in Ancient Rome' and Thornton's 'Eros'.