According to a source, "almond (64 percent market share), soy (13 percent market share) and coconut (12 percent market share)"
http://www.mintel.com/press-centre/food-and-drink/us-non-dai...
EDIT: I should add, for those interested, that this dominance is perhaps less strange when noting that California alone produces around 80% of the world's almonds.
Milk is subsidised in many markets, either directly or indirectly; but the demand side makes a big difference too. Also, things are often priced to what people will pay...
It was like a negative aha-moment, a taste that was always there but I never noticed it, when it finally clicked, and I found out it was a fishy taste soy milk pretty much died for me.
I also like rice-soy milk, it doesn't have the strange after tastes of soy milk, but it's just so thin, hehe.
2-3 years ago many grocery stores added other milk alternatives. While I think almond milk is the best, oat milk is the second place but much cheaper.
Generally, milk is heavily subsidized in Germany and alternatives are 2-4 times more expensive, so I don't know if this a little hype or the start of a lasting change. Milk costs like 0,60€ a liter, oat milk costs 1,50€ and organic almond milk can cost up to 4€ a liter.