Are there culinary uses for the water left from peeling almonds?

Generally, there is no reason not to use it. However, I'm hard pressed to think of a good place, generally because good cooking prefers other, stronger flavored liquids instead of water.

An application where you can have the flavor on its own would be making ayran or a lassi. I think it would be an improvement over plain-water-ayran.

For other uses, just substitute plain water to get a slight nutty hint. I like to pair rice with nuts, so you could use it instead of pure water to cook rice. Or add it to a pot of stock you are making - with a complex stock of a meat and several vegetables, it will be too subtle a taste to register consciously, but will enrich the flavor as a whole. For a simpler stock (e.g. just chicken with classic mirepoix) the taste of almonds can get too strong, depending on the quantity you use.

You could use it when making horchata. It is a drink made with rice, cinnamon, sugar and water. Almonds and/or milk are used in some variants. Use your almond flavoured water instead of plain water when soaking the rice. This recipe might give you a starting point:

http://www.foodnetwork.com/recipes/gale-gand/horchata-recipe/index.html

I used up a pot full of almond water because I refused to throw all that good stuff away. I first drank it cold from the fridge when I got thirsty :) It's an interesting mild flavor, but it might take some getting used to. I used some more to make an apple drink (crush apples in blender, slowly add this water to it until you get the desired consistency). I used up the last cups to make rice. In my opinion, that was the best use (although least exciting).

P.S.: The water tends to ferment over time. Doesn't taste terrible but it might not be the greatest idea to consume that.