Ásatrú, also known sometimes as Odinism, has its basis in Germanic Neopaganism but sprouts tentacles off in many different directions with many different factions, many of whom don't always see eye-to-eye.
In very general terms, Asatru is a polytheistic faith, centered around worship of the ancient Norse Gods and Goddesses. Many of the names of these gods and goddesses remain part of our modern culture, such as in the days of the week: Wednesday is Woden's (Odin/Wotan's) Day, Thursday is Thor's Day, Friday is Freya's Day. Ásatrú - the true Ásatrú - is open to everyone, regardless of gender, race, color, ethnicity, national origin, language, sexual orientation, or any other divisive criteria.
The current leading Ásatrú organization seems to be Ásatrú Alliance, which succeeded something called the Asatru Free Assembly which was also succeeded by something else called the Asatru Folk Assembly. According to Wikipedia, the Asatru Alliance was founded by Michael J. Murray, the former Vice-President of something else yet again, called The Odinist Fellowship.
Confused? Me too. It's like trying to sort out a bucket of nightcrawlers. At night. Let's not even get into the more hardcore "Odinist" types like The Odin Brotherhood, The Odinic Rite, The Odinist Fellowship, Holy Nation of Odin, and Wotanism.
The problem with Asatru/Odinism is that it's too "open source" a concept - the danger with starting a religious organization that you can't maintain strict control over is that before you know it, all kinds of kooks are starting rogue versions of your religion, and using it for unsavory purposes that you didn't intend. And so we have people out there calling themselves Odin worshippers who couldn't be more different from one another, ranging from young left-wing hippie girls to ultra-right-wing shaven-headed nutcases. Still others are merely attracted to the swords and the costumes and the mead, and would probably be better off visiting a Rennaissance Fair than changing their religion.
Because of its anglo-centric nature, it has attracted both gentle Wiccans and psychotic "White Power" supremacists - neither of which, needless to say, want to have anything to do with each other. For the most part, the peaceful ones just want to be left alone, and it's the stupid skinheads with skulls tattooed on their necks who stir up trouble and give the larger body of Ásatrú a major PR liability.
It's enough to make an Ásatrú practitioner throw up their hands and say "to hell with it, I'm just going to go over here and start my own personal Scandinavian-flavored thing and stop using the names "Asatru" or "Odinist" entirely".
And many, in fact, are increasingly doing just that, preferring to keep it vague and unaffiliated, and just calling themselves "heathen" or "pre-Christian" and leaving it at that. Many keep their groups tightly-knit among a close circles of family and friends, and have moved past the idea of belonging to over-arching all-encompassing organizations where you end up side by side with people whose reasons for interest in all things Germanic may be more sinister than yours.
Kentucky has a local Ásatrú chapter located in Hazard, called the Kentucky Ásatrú Alliance. According to their website (which is currently offline for some reason):
"More and more people are moving away from universal religions that assert their path as the "one and only right way" for all humanity, and returing to the tribal paths of their own ancestors. These ancestral "folk ways" are after all, an expression of the totality of the people who developed [with] them as ways of understanding and expressing existence. Since much of our being (both physical and psychological) is passed on to us from our ancestors, their natural spirituality is surely the most compatible with our own instinctual being."
Another site of theirs, FrithNet, is still online but doesn't look to have been updated in over a year. And it in turn links to a worldwide Ásatrú auction site called FeeFum, which shows a little more activity, but not much, and the items being auctioned are predominantly jewelry. And yet another site, Samfelag, ostensibly for networking, also seems little-used.
Does this mean that the Ásatrú faith is in decline? No, far from it. I'd say it most likely means that the kind of people drawn to true Ásatrú would be the kind of people who don't spend a whole lot of time fiddling around on the internet - and for that, I say more power to 'em. Then again, they are on Facebook, which is unfortunate.)
Other Ásatrú organizations around the world seem to still exist - such as Asatru Alliance in Arizona, Asatru Folk Assembly (though their site still says 2008 at the bottom), The Troth in Connecticut, Irminsul Ættir in Washington state, and The Canadian Asatru Portal, who provide an exhaustive array of further Asatru links here.
Given that most seem to be sticklers for historical authenticity, something tells me they're not going to like the upcoming Thor movie, which bases itself on the highly off-model Marvel Comics version and takes it even further off-model.