There is an extremely easy one which is naturally vegan - i.e it wasn't made for vegans, it just happens to not have milk or eggs in. You can substitute chocolate for another flavour, e.g. use lemon instead - just adjust the amount of liquid appropriately. I know it seems like a lot of oil but hey, it is cake, and it makes it deliciously moist!
The raising agent is the baking soda which reacts with the vinegar. You can't taste the vinegar in the finished cake. However if you're worried about that you can buy an egg substitute from somewhere like Holland and Barrett and use that instead.
I have made this cake dozens of times and you definitely need to make it in two batches and do a layer cake. If you put the whole lot in one batch it won't rise enough and will be raw in the middle. I suppose you could also make a very big flat cake to spread the mixture out.
From Boutell.com:
Ingredients:
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3 cups flour (680 grams)
2 cups sugar (450 grams)
6 tablespoons cocoa (100 grams)
2 teaspoons baking soda (10 cc's = 10 ml)
1 teaspoon salt (5 cc's = 5 ml)
3/4 cup vegetable oil (200 cc's)
2 tablespoon vinegar (30 cc's)
2 teaspoon vanilla (10 cc's)
2 cup cold water (480 cc's)
Instructions:
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Mix the dry ingredients. Add the wet ingredients. Stir until smooth. Bake at 350 degrees for 30 minutes. Makes two layers of a two-layer 9-inch or 8-inch round cake, or one small sheet cake. When cool, frost it.