I've always been an avid reader of old myths, fairy tales, and folk stories, as a child I was just as likely to be reading a book of Norse myths as I was a superhero comic book or science fiction novel. American culture takes a lot from Greek myths, their legends and heroes and stories encoded in our consciousness (mostly thanks to the influence of the French and English, both of whom considered themselves the inheritors of the Greek cultural legacy). We think of people having "Herculean" strength, most people's image of God as a bearded man who sits in the clouds come from the Greek depictions of Zeus, and even common phrases like "satire" come from satyrs, the bawdy and untrustworthy half-goat-half-men of Greek myth.

But that said, all that doesn't mean Greek myths are the only ones worth talking about. As mentioned above, I adore Norse mythology, and I also quite like Arab and Persian folktales as found in the One Thousand and One Nights. Recently I read a fantastic collection of fairy tales by the English writer Angela Carter (Angela Carter's Fairy Tales) which scours the mythologies of all sorts of cultures, from Europe but also from other corners such as Sub Saharan Africa, Southeast Asia, and the Inuit people.

I'm interested to hear what other people's favorite mythological systems are.