I'm a mythology nut. I've been that way for a long time, and it comes out in my writing (I mean, I'm writing a book filled with Trickster gods right now). But one of the things I find most fascinating about mythology is the archetypes behind the stories.
For example, almost every culture has some sort of creation story. Whether the gods created people from mud or corn or starlight will differ from culture to culture, but the general idea remains the same. It's fascinating to me to look at all the different takes on the same idea, depending on where the culture grew and how it was influenced by the world around it.
But mythology isn't just great for leisure reading or psychological study. It's a great place to find inspiration, too. Looking for a religion for your aliens? Why not study Japanese myth for inspiration? Need a new god for your not-Tolkien-esque elves? Try looking at Polynesian stories for ideas.
Do note that I don't recommend stealing the myths themselves (unless you're writing about those particular peoples/myths), but looking at how different cultures see the world can be a fascinating insight into how the human brain works. And it's a great exercise in looking at archetypes and how they can be used in different ways. Compare Loki and Anansi, both Trickster archetypes, to see what I mean. Or, if you'd rather, look at Zeus and Odin--they're both the Strong Leader/Father-type archetypes, but their stories are very different.
There are so many different cultures and different mythologies in the world. Some of them are harder to research than others (just look at the number of Greek myth books versus the number of Maori myth books, for example), but I think all of them are worth our time as writers.
When Emily's not writing or drooling over mythology books, she's probably playing Pokémon or getting ready for Comic Con. Find her at emilykaysinger.com or on Twitter @EmilyKSinger.