nutcake's recipe above is what I've always used, but I add a couple Tablespoons of hersheys chocolate syrup to the batter. It seems to keep it a little moister and adds to the flavor nicely.

There are many versions of poor man's chocolate cake all over the internet. I would likely increase the cocoa powder by a few TBSP You may google vegan desserts, which don't use eggs, then use butter and milk instead of soy if you like.
Title: Poor Man'S Chocolate Cake

3 c flour
2 c sugar
6 tb cocoa
2 ts baking soda
1 ts salt
12 tb oil
2 tb vinegar
2 ts vanilla
2 c cold water

In greased pan 13x9, mix all ingredients until smooth. Bake 350ø 40 to 45 minutes. Do not overbake. Frost if desired. (see below)

Poor Man'S Frosting -- Yield: 4 To 6 Servings

Ingredients

1 c milk
1/4 c flour
1 dash salt
1 c sugar
1/2 c margarine
1/2 c vegetable shortening - such as crisco
1 t. vanilla

In saucepan, cook milk, flour & salt till thick. Cool well. In small mixing bowl add sugar, margarine & shortening. Beat well with electric mixer. Add flour mixture & 1 t. vanilla. Beat till fluffy and stiff like whipped cream.

Here's our favourite chocolate cake, which happens to be vegan: http://www.food52.com/recipes/3057_fudgy_chocolate_cake

And this cupcake is egg-free also! http://www.food52.com/recipes/7731_pumpkin_cupcakes_with_goat_cheese_frosting

Sometimes recipes use buttermilk (or vinegar) plus baking soda in lieu of eggs for leavening. If you google "buttermilk cake no eggs" you will find recipes like this:
http://foodiemommy.blogspot.com/2010/05/chocolate-buttermilk-cake-by-dessert.html
or this (even though this one doesn't even have buttermilk...):
http://www.epicurious.com/recipes/food/views/Old-Fashioned-Chocolate-Cake-with-Cocoa-Frosting-755

You could make any vegan dessert...vegweb.com has a ton of recipes you could check out. Or you can just do a general google search for "vegan cake"...there are a lot of vegan food blogs out there!

Shortbread cookies or trifle or an icebox cake!