You all seem like the types of people who might have some input…
I’ve been rereading Stephen Fry’s “Mythos” and “Heroes.” I’ve read Neil Gaiman’s Norse mythology book several times.
Does anyone have recommendations for similar tellings of myths from other places? Egypt? India? China? Japan? South America? Native America? Anything?
Enjoyed Neil Gaiman’s Norse mythology book as well, and would be interested in hearing other peoples recommendations. 
The Pantheon Fairy Tale and Folklore Library is a great place to start for a lot of good mythology. Their Norse myth book by Kevin Crossley-Holland is still my favorite version of the myths.
For fairy tale encyclopedias its hard to beat the acknowledged mistress of the field, Katharine Briggs.
I’ll seek small-run books on more obscure myths and folklore as well. One I recently obtained was a book from Iceland on their Yule Lads tradition.
And finally, for retellings there has been a recent series of books from Canongate with modern writers doing very unique takes on mythology. I especially recommend Margaret Atwood’s take on The Odyssey (The Penelopiad) and Victor Pelevin’s version of the Labyrinth of the Minotaur (The Helmet Of Horror).
Well, I guess there’s Paul Zumthor’s Essay on Medieval Poetry, which IIRC is largely concerned with Arthurian legends in Chrétien de Troyes and others on the continent.
For a true attempt at re-telling, or re-imagining the Arthurian tales, Jack Spicer’s The Holy Grail (reprinted in the paperback The Collected Books of Jack Spicer) is a treat that one shouldn’t deny oneself.
I can’t think of any good ones for Greek and Roman mythology, except for older resources like Edith Hamilton. However, if you can make sense of Hermann Broch’s The Death of Virgil, then I’ve heard it’s quite a little novel.
I guess for some sweeping, sort of academic overviews, two major ones are Auerbach’s Mimesis: The Representation of Reality in Western Literature and Lovejoy’s The Great Chain of Being. But I don’t think that’s really what you’re after, and I couldn’t really recommend either unless you’re pretty bored.
I like the suggestions by others, though, and I don’t know any of them, so I’ll have to get around to those myself.
If you’re wanting actual reading material about the myths and beliefs of other cultures, The Sacred East gives a good overview of Hinduism, Buddhism, Shinto, Confucianism and Taoism.
I have a book called World Mythology by Roy Willis that will give you summaries of pretty much every culture you could think of as far as mythological stories go.
If you’re wanting novels that make use of mythologies, there’s a great one by Roger Zelazny called The Lord of Light that plays around with Hindu mythologies.
If you want the real stuff, there are translations, probably available for free digitally, of the Ramayana and the Bhagavad Gita.
If you want more, I can give you more. World religions is a major interest of mine. 
Not strictly mythology, but the Histories of Herodotus makes for some interesting reading. Especially the account about how Hercules once met a woman whose lower half was the body of a snake and she wanted his snake in her snake.
I hear The Lion, The Witch, and The Wardrobe is a retelling of a pretty popular religious text. Or, at least, people are seeing similarities buried within it.
The entire Chronicles of Narnia are. If it wasn’t apparent by Voyage of the Dawn Treader then The Last Battle really clears it up.
The classic Greek mythology (with a little Norse mixed in) book is Edith Hamilton’s Mythology.
John Steinbeck got partway through a retelling of King Arthur.
I’m actually working on an urban fantasy novel which will use beings from various mythologies. I’m pretty stuck on the final climax scene at the moment, but still hoping to finish it and see what I need to do to start shopping it around for possible publication. If I finish it I’ll let you know when it gets published and you can see if you’d like to read it.
I’m glad to see some lesser-known (in English-dominant countries at least) mythologies getting more exposure these days. The tales of Reynard the Fox and those of Anansi the Spider are enjoying a popular resurgence. The Mabinogion, never really out of fashion, is back in the public conscious again. And I am hopeful that the Kalevala will experience an uptick as well.
I’m throwing Bulfinch’s Mythology as a great starting resource.
Edit: think I might have misunderstood your aim
I wasn’t sure I understood precisely what was meant either so I answered it in every way I could interpret it. 
Does it have a stargate?
No. I’m focusing mainly on Greek, Roman, and Slavic mythology to start off with. AKA actual mythology. 
Besides, the correct question (as we all know) is “Does it have a thunderdome?”
If Godzilla is a thunder lizard, then Gamera is a thunderdome.
Fairy tales rather than ‘myths’, but I’ve been enjoying Mercedes Lackey’s ‘Elemental Masters’ and ‘500 Kingdoms’ series. Although there is some ‘myth’ stuff mixed in.