Here's a passable pancake/crepe recipe that doesn't require eggs and works perfectly well with vegetable milks (it works with animal milks too). You can make sweet pancakes by adding sugar (as much as you like) or savory ones, by adding salt. I usually make a kind of 'neutral' pancacke by adding a little salt and sugar. That's how I learned to do it from asking how Russian 'blini' are made and the result goes well with savoury and sweet fillings. The quantities I give might need adjusted a little to achieve the correct consistency for your needs. I like very thin crepe-style pancakes and I tend to go for a thin mixture with a consistency akin to unwhipped double-cream. A little bit more liquid will probably be required for that. You can experiment with different mixes, but thicker mixes will not be as successfull as they would be with the addition of eggs as a raising agent.
I have had success making thicker pancakes by using less water in the mix and adding a little activated yeast and leaving it to sit for half an hour before using. Don't stir the mixture after this as the tiny bubbles which have gathered will be lost and they're what provide the lift. Baking powder is an option too, but I find it makes chalky-tasting pancakes that go stale quickly.
This should do about 8-10 large pancakes/crepes, but it will ultimately depend on the size of pan you use. I recommend using a soup ladle to spoon the mixture into the pan.
Ingredients
About 1.5 cups of plain flour
About 2 cups(+/-) of soya or coconut mik
2 table spoons of oil/melted margarine
A pinch or two of sugar and/or salt
Mix the flour, sugar/salt and water together well and then add the oil gradually while stirring. Beat the mixture well until there are no lumps.
Heat a frying pan until it is hot (no oil needed) and then pour in a ladle-ful (or about 3-4 tablespoons) of mixture and swirl it about by tilting the pan in various directions. Cook until bubbles appear over the whole surface and the edge turns golden-brown (about two minutes), then loosen the pancake with a spatula and flip it over and cook for another minute or so. Turn the heat up or down as needed: once the pan is hot through, a medium setting will be about right. You're first pancake or two might not be very good, but once the heat is constant, you'll be knocking them out like a pro.