If the path before you is clear, you're probably on someone else's.
There's a horrifying tendency for most writers to dig into the stuff they grew up with - Biblical, Egyptian, Greek and Roman mythology - and look no further. I can testify that back in my school days, I didn't even realize there was more to mythology than that. It's probably a bit different for school children now, but back then, things were still stuck in the Occident, and to hell with the rest of the world.
It wasn't until I got to college that I realized there was a whole other three-quarters of the world chock full of some really incredible mythology. It started with the Sumerian stuff. I remember reading The Epic of Gilgamesh and feeling giddy. I recognized Enkidu as the panther from Salvatore's books. And then I started peeling back the Arabian and Oriental myths, and man....
Later, I discovered that in my own back yard, there was some incredible mythology to be had: Navajo creation stories, Hopi kachinas, Kiowa sun stories, an endless list. My gods, why would I want to limit myself to Greece, Rome, Egypt and Israel with all this other stuff out there? Why did so many authors tread the mill of Arthurian legends when the Norse had some kick-ass legends of kingship, love and betrayal that hadn't already been picked to the bone?
I finally figured out the answer: it's safe and easy, that's why.
Moving into lesser-known mythologies is a dangerous road to take, as the Occidental mind sometimes can't comprehend the Oriental, animistic, shamanistic and other traditions, and so aren't as prepared to understand the story. That's why those who draw on other mythologies and don't want to blatantly Westernize them have to be far better storytellers than otherwise if they want to reach a wide audience in the West. While the underlying patterns might be familiar - loves won, battles fought, boons claimed, and so forth - the way those patterns are woven are different and sometimes incomprehensible at first glance. It takes a lot of work to decipher those patterns for untrained minds, and if the author's not careful, it ends up being a thinly fictionalized essay on other beliefs rather than a mythologically-informed story.
Also, there's a lot less research involved, and far fewer resources available. I discovered this while trying to research Odin. You can get books dealing specifically with the major gods and goddesses of most Occidental traditions, but gods forbid you should need that kind of detail for a lesser-known deity or tale. It takes a lot of digging through large and scary (and sometimes damned expensive) books to get the information needed to create a rich and detailed story based on non-mainstream myths. In light of that, it's no wonder most authors turn to the easier stuff.
But I challenge you to take the dangerous roads, the untrodden paths and the unmapped territories. You'll find rich rewards there. Some very extraordinary modern works have been based on non-Occidental myths. The world's in the mood for things less parochial, more exotic, than yet another retelling of Arthurian legend. Although they're always in the mood for more of that, so don't sweat it if you skip this section.
For those willing to wander off into the wilderness with me, let's go into some foreign places.
A good place to start is "A funny thing happened...." There's this perception that if something's based on myth, it's got to be serious and intellectual and really, really profound. Not true. I mean, come on, how can you take Zeus's womanizing seriously? I can assure you the Greeks didn't, not really. So if you want to step out of the Occidental mindset but don't want to leave the Occident, simply look for the humor.
You can accomplish this in one of two ways. You can lampoon an otherwise serious myth, which Christopher Moore did to brilliant effect with Jesus' "lost years" in Lamb: The Gospel According to Biff, Christ's Childhood Pal. Look for the comedic possibilities in the Iliad, Lucifer's fall, anything. It doesn't matter how serious the subject is, you can always find something funny about it.
Or you can simply go with a myth that was funny to begin with. Every mythology has tricksters, whose stories are outright comedy. Neil Gaiman took the cycle of African stories of Ananzi and created Ananzi Boys from them. And as you delve in to world mythology, you'll find some cultures that seem to have a more amused outlook on life, the Universe and everything than we're used to. There's no shortage of mythologies whose major comment is "Funny ol' world, isn't it?"
If, however, you don't plan to write humor, there's plenty of serious stuff out there. You don't get much more serious than some of the South American and Mexican mythologies, in which the world's about to end and will end sooner if one doesn't tear out twenty thousand hearts a year. Delve into anthropology for a look into the minds of tiny , obscure tribes. Ancient Sumeria's also a good place for the grim stuff. According to them, humanity was created to be slaves of the gods. All kinds of potential for very serious, meaningful stories based on an outlook like that.
For sheer beauty, try some of the African and Oriental myths. Hinduism's a good place to go if you want to find a mythic structure that celebrates life. One of their best-beloved stories is Krishna's adventures with a lot of very willing young women. And you'll seldom find a mythology more balanced and serene than Taoism.
There's also scary stuff. If you're trying to write horror without camp, a lot of the old mythologies will provide you with story material that will keep you awake with the lights on for a very, very long time. There's no end to the danger and monsters.
Don't want to go for the great big myths? Fine. Explore folk tales and urban legends. These, too, are myths: they explain something about the world and follow established patterns. They're fertile ground for mythic storytelling even though they don't look like myths on the surface.
It's a big, big world out there, with plenty of myths that few people have ever heard of to base stories around. But say you don't want to use other people's myths, even disguised. Say you want to create your own. Or maybe you're writing fantasy or science fiction, and you don't want the aliens or magical creatures to have the same stories as earth people do. How do you create a new mythology?
First, you have to understand precisely what myth is and how it's generated. This is where you stuff yourself full of comparative mythology. After a bit, you'll notice a pattern: all mythology is based around things that are important to all people. Only the cosmetic details are different. At core, all myth deals with the things that people desire or fear most: life, death, love, conflict...
There's where you start. Identify which things are most important for your aliens or other creatures. Maybe death to them is no big deal. Maybe they don't agonize about the meaning of life. In that case, they won't have those types of myths. But what's really important to them is food. They're obsessed by it: where it comes from, why it's eaten, why it tastes good, etc. Once you've identified the important things like that, you can start building the mythologies they might have about such things.
Keep in mind the following important points while creating new mythologies:
1. Place is important. The climate, terrain, and other details of where people live affects their myths.
2. Social structure impacts myth. The Sumerians, who lived in a very rigid agrarian society, have myths that are fundamentally different from tribal and nomadic societies. So make sure you know if the people you're creating myths for are nomadic or settled, hunters or planters, and know how that will impact their mythologies.
3. Biology. All of our myths are necessarily filtered through our biological realities. So will your beings'. It's hard to think like a quadruped or a fish, but do try.
4. Age and education. Old, established societies with a lot of scientific knowledge have different myths than younger ones, or those who don't have science. There's a difference between oral and written traditions, too.
5. Attitude. The Greeks had fallible gods, and the humanists among them placed humanity on a higher level than those gods. Societies that de-emphasize the importance of humans compared to nature or the gods tell their myths differently. So know what your people's attitude to people in relation to the world around them is.
Once you've figured out what myths they might have, make sure you get the language and tone right. The more myth you read, the better you'll do with this. Myths aren't told the same way anecdotes are. Their language may be simple or sophisticated, but it's not like ordinary language. Give it a special flavor all its own. Remember that most fairy tales start with "Once upon a time..." There's a reason for that. Find the equivalent to "Once upon a time" for your made-up myths and stick to it. Myth is all about pattern and structure - you'll have to create those for the myths you make up.
And yes, it's perfectly okay to make a chimera from bits of many different myths. Just make sure you smooth out all of the joins so it looks like a whole, unique tradition in its own right instead of a sloppy Frankenstein with all of the stitches showing.
There's plenty to help you out, whether you're wanting to use established myths or make up your own.
PART TWO RESOURCES:
The Masks of God Series by Joseph Campbell. This is comprised of four volumes: Primitive Mythology, Oriental Mythology, Occidental Mythology, and Creative Mythology. There is no better survey of all that's out there than this.
Transformations of Myth Through Time by Joseph Campbell. If you want to modernize old myths or create myths of your own, there's no better book to help you understand how myths mutate due to changing circumstances.
Parallel Myths by J.F. Bierlein. For those who want the-same-only-different themes, this is a great book. It deals with a lot of common themes in world mythologies. It will also help you pinpoint those interests people have in common.
The Enchanted World Series by Time-Life Books. Gorgeously illustrated and wonderfully told tales from all around the world. This series contains just about anything you'll ever need when it comes to myths, from folktales to major mythologies, and they're told as fact, not fiction, which makes it all the more interesting. You can almost believe that once upon a time, all this stuff really happened....