Here's my family's recipe for Wacky Cake. It requires no eggs. I know no other cake recipes that includes vinegar. You don't have to grease your baking pan. In fact, you can mix it in your baking pan, thus saving yourself one less bowl to clean.
1-1/2 Cup flour
1 Cup sugar
1 t. baking soda
3 T. cocoa
1/4 t. salt
1 t. vanilla
1 t. vinegar
6 T. melted butter
1 Cup warm water
Sift all dry ingredients into an 8" cake pan, or into a 9" x 13" pan if you double the recipe.
Make three holes in the flour mixture for vanilla, vinegar an butter.
Pour warm water over all.
Mix well an bake at 350 degrees for 30 minutes.
Frost if you want to.
To make cupcakes mix in a bowl. A single batch will make about 12 cupcakes.
Our family got this recipe from our Morton Grove neighbor Eunice Mattes.