I finally finished American Gods, having started it nearly a year ago! For anyone who hasn't read it, there are major spoilers ahead.
The basic premise of American Gods is that, as in the Discworld and, apparently (according to Clash of the Titans) in Ancient Greece, the gods are brought into existence by the force of people's belief, and that the millions of immigrants to America brought their gods (and leprechauns, and pixies, and kobolds, whatever they are, and various other assorted supernatural or divine creatures) with them.
Now, obviously, none of the main characters are Classical gods because by the time Greeks and Italians made it to America they were Christian. Many of the central characters are Norse gods, since it is generally believed that Vikings travelled across to America in the Dark Ages. Gaiman also includes several Egyptian deities (primarily Horus, Bast, Anubis and Thoth) on the grounds that Egyptians were travelling to America in ancient times - this, I confess, I find rather less plausible and I have a sneaking suspicion he just wanted to use the Egyptian mythology and imagery. When the central character dies part way through (he gets better) he wonders why he undergoes an Egyptian journey into death, complete with the weighing of his soul against a feather under threat of being eaten, and why he didn't get St Peter and the pearly gates, since that would be his cultural expectation, and is told that although he didn't believe in them, they believed in him. All of which reinforces my opinion that the real reason is just that Egyptian imagery is cooler!
There are also solid, important reasons for taking a more subtle approach to the Judeao-Christian imagery, though the nature of the story means it could hardly be left out. It is fairly safe to assume that the number of people who actually believe in Odin or Thoth are fairly small, if they exist at all, so those characters are free to be reinterpreted without taking pot shots at people's deeply held beliefs. Most of the mythologies present here, I confess, I have very little knowledge of - I have a vague knowledge of Norse mythology and I know Egyptian mythology of course, but the mythology I know best is classical, which isn't here. I don't know how far current beliefs are reflected in some of the other characters, especially the Native American characters, but I sense that there is an emphasis on the older, more forgetten gods, which fits the story anyway, since it is about gods who are old and neglected - modern religious figures are assumed to be living somewhere where they are worshipped, not in America.
Jesus does make an appearance though, in a suitably subtle (and unnamed) fashion, as a friendly and extremely successful carpenter who has rather a lot in common with Shadow, the protagonist. The whole scene is dealt with very cleverly, as it's not especially offensive to Christians, but at the same time it does not shy away from including the Christians deities as mythical gods among the rest. Christian imagery is also appropriated at times, chiefly in the themes of death and resurrection and the stabbing of Shadow while he hangs, dying, from a tree, while Easter appears as the Germanic pagan goddess Eostre, whose festival was in April and who in reality may or may not have been invented by the Venerable/Venomous (depending on your point of view) Bede.
The Venerable/Venomous Bede
There are some references to Classical deities, usually brief mentions from other characters. Mithras, the 'army brat' apparently had his birthday stolen by Jesus, a reference to some of the origins of the Christmas festival, though Christmas as we know it is composed of quite a few different influences and this is a bit of an over-simplification. At one point we meet 'Media', one of the new gods, and someone asks if she's the one who killed her children - no, says another (that was Medea, who wasn't actually a goddess, though she had divine relatives) but implies that the two are very similar. Presumably this is intended to imply that Media can be deadly to her viewers. Bacchus gets a very brief mention and somehow the emperor Hadrian's deified beloved, Antinous, has made it over to America, though how he managed this is not explained.
I also thought I spotted the ghost of the Golden Bough that so fascinated JG Frazer at one point (an early twetieth century mythologist/armchair anthropologist who thought every single religion anywhere, ever was about the death and resurrection of the god of vegetation and who thought that a particular rather odd and violent Roman tradition involvoing a tree and the golden bough that must be plucked by Aeneas before entering the underworld was the key to it all). My familiarity with Norse mythology is too vague for me to be sure whether this was a reference to the Aeneid (and Frazer) or a Norse thing, but it definitely seemed a little bit Frazerian to me.
The book does assume a lot of knowledge (or, possibly, willingness to look things up) as references like these are scattered throughout without explanation. I missed many more of them than I caught (though I was quite pleased with myself for knowing who Louise Brooks was!). My knowledge of mythologies outside Europe is pretty mch non-existent and my knowledge of America is patchy and gleaned mostly from TV, so there were a lot of things that went over my head. On the one hand, this technique allows the reader to really empathise with Shadow in his confusion at this new and strange world (and those readers who are familiar with all the requisite myth systems can fell thoroughly smug and superior, which is always fun!). On the other hand, it was rather frustrasting knowing that there was a lot more to what was going on, but that I didn't know what it was.
Louise Brooks. In case you were wondering!
Overall, I enjoyed the book a lot, though I didn't really get into it until quite far through (and there was a fair amount of focus on a certain male area - but I think that's true of mythology as well, so fair enough). And although I haven't read Twilight: Breaking Dawn, I have read summaries and reviews of it, and found myself drawing some rather unexpected comparisons at the end. Gaiman is a brilliant writer though, and the short stories telling tales of particular gods and immigrants were often the most gripping parts - though I was also genuinely fascinated by the character of Shadow and by Laura. The final twists were pretty bog-standard, but done well and I must go and see the House on the Rock some day.
This is not really a book about mythology, but a book about America, and for someone like myself, who has never been further than New York, it makes fascinating reading. Unfortunately, however, that focus on America is what keeps the Classics at bay, for the Classical gods never made it to America (outside of Percy Jackson) - they remain the the Old World and, even here in Europe, are more frequently referenced as an element of our past than our present. American Gods is about the junction and the tension between past and present, about what changes and what stays the same, and something frequently (if incorrectly, in my opinion) categorised firmly with things that are of the past, like Classics, perhaps doesn't fit as well as the other mythologies that Gaiman focuses on.
(By the way and on a totally unrelated subject, did everyone - in the UK anyway - see the finale to Ashes to Ashes the other night? It was brilliant!)
Edited to add: TV Tropes has cleared up the mystery of Shadow's real name, which my hazy memory of Norse mythology had obscured - Baldur. So the stick and the stabbing may also relate to mistletoe.