I’m dairy intolerant so I don’t drink any kind of animal milk at all. There are four alternatives I’ve come across.
Soya milk: Easy to find, tastes very vegetable-y, some people have allergy issues with soya and there are concerns about genetically-modified soya.
Rice milk: relatively tasteless, goes well with anything. There are some ethical issues surrounding the leading brand’s involvement with Wal-mart, Exxon Mobil and Monsanto; companies with a poor ethical & environmental record.
Oat milk: very oaty taste, which I like but not many people do.
Almond milk: said to be the best but so expensive here that I haven’t actually tried it yet.
Of these my favourite is oat milk.
Rice milk is easy to make: recipe (and an explanation of why Rice Dream is bad) is here: http://www.veganreader.com/2009/05/17/how-to-make-rice-milk-and-stop-supporting-rice-dream/
Oat milk is made in exactly the same way, just substitute oats for rice in the recipe.