My parents make this cake all the time (in fact, this is the cake we had at our wedding). It is also frequently requested for holidays and birthdays.

Cake ingredients

1 1/4 cups flour
1 cup sugar
1/3 cup unsweetened cocoa powder
1 tsp baking soda
1/2 tsp salt
1 cup warm water
1 tsp vanilla extract
1/3 cup vegetable oil
1 tsp distilled white or apple cider vinegar

Chocolate glaze

1/2 cup sugar
4 tbsp margarine
2 tbsp soy milk
2 tbsp unsweetened cocoa powder
2 tsp vanilla extract

Note: if you don't care to make it vegan, or don't have soy milk or margarine, you can use butter in place of the margarine, and whatever milk you prefer in place of the soy.

Instructions

1. Preheat the oven to 350 degrees F. In an 8x8 square pan, mix together flour, sugar, cocoa, baking soda, and salt with a fork, making sure it is really blended together. Add the water, vanilla, oil, and vinegar, and mix together so that it's really blended together. Use a spatula to scrape down the sides if necessary.
2. Place in oven and bake for about 30 minutes, or until a knife comes out clean. Cool on a rack completely (2 hours).
3. To make the glaze: in a small saucepan, bring sugar, margarine, milk, and cocoa to a boil. Stir frequently; then reduce heat to a simmer for 2 minutes, stirring constantly. Remove from heat and stir for another 5 minutes.
4. Add vanilla, stir, and immediately pour onto cake. Glaze dries really quickly, so spread it immediately. Cool for an 1 hour.

Source: Instructables