You can typically substitute oil for any butter and water for milk in a cake recipe but you'll get a moister outcome. Frosting is a little harder to come by, there is always the option of subbing margarine for butter although that has quite a bit of trans fat. Most of the frostings require a solid fat or cream, basic icing does not if you want a glaze but it depends on how much you want a traditional cake vs something with say a lemon glaze.

Oh this one is right up my ally. I bake 95% dairy-free for a variety of reasons, and you can never tell. I use mostly margarine - but you need a good solid stick brand - I use Fleischmann's unsalted. I also use soy milk and non-dairy cream and it really comes out great every time.

Here's my recipe for a fabulous and dairy-free yellow layer cake and chocolate frosting.

Cake:

4 cups plus 2 tablespoons flour
2 teaspoons baking powder
1 1/2 teaspoons baking soda
1 teaspoon salt
2 sticks margarine, softened
2 cups sugar
2 teaspoons pure vanilla extract
4 large eggs, at room temperature
2 cups soy milk mixed with 2 tbsps lemon juice (buttermilk substitute)

In a large mixing bowl, beat butter and sugar in a large bowl with an electric mixer until pale and fluffyAdd in vanilla and eggs 1 at a time, beating well.
Gradually mix in milk mixture until just combined (mixture will look curdled).
Gradually mix in flour, baking powder, baking soda and salt.

Spread batter evenly in two 9 inch round or 8 inch square cake pans.Bake 35 to 40 minutes on 350 F.
Cool in pan on a rack 10 minutes, then invert.

Frosting:
12 ounces semisweet chocolate, finely chopped - trader joe's sells great chips that I use.
3/4 cup heavy cream - rich's whip is a perfect subsitute.
1 1/2 tbsps sugar
1 1/2 tbsps light corn syrup
3 tbsp margarine

Bring the cream, sugar and corn syrup to a boil over low heat, mixing until well combined.
Remove from heat and whisk in chocolate until melted and smooth. Add in butter until stir until melted and combined. Let sit until comes to room temperature. Do not refrigerate before use - it will harden. Keep extra in the fridge.

sally599 triggered my memory of Alton Brown's episode of the "avocado experiment" because he used avocados for the fat content, most notably in ice cream. that might be an avenue worth exploring -- and if you do, let us know your results!

the vegan frosting in the babycakes nyc cookbook is delicious. I would highly recommend it for cupcakes and cakes -- I like both the vanilla and the chocolate

http://www.babycakesnyc.com/books.html

Expanding on the avocado idea, Joy the Baker has a recipe for Vegan Chocolate Avocado Cake on her blog: http://www.joythebaker.com/blog/2009/07/vegan-chocolate-avocado-cake/#more-930

Perhaps a flourless chocolate cake (too many recipes to list--claudia roden has, if memory serves, one with cocoa and/or nondairy chocolate) with a chocolate raspberry or marmelade glaze. alternatively, an orange-almond-egg cake (also claudia roden) with a citrus glaze.

Check out Vegan Cupcakes take over the World. Lots of yummy recipes!

The Vegan With a Vengeance cookbook has a carrot cake recipe (they have several cake recipes but I can vouch for this one 100%) with frosting using coconut milk and earth balance spread as a binder and it is insanely delicious (and not overwhelmingly coconut-y). It's a really delicious recipe if you like carrot cake. I found a copy of it here:

http://unrelentingambiguity.wordpress.com/2008/01/19/delicious-ginger-macadamia-coconut-carrot-cake-recipe/

Though I haven't tried these recipes, Karina's Kitchen has a load of vegan (and gluten-free) recipes. Here's a link to the index: http://glutenfreegoddess.blogspot.com/2008/07/vegan-vegetarian-recipe-index.html

Hope this helps you!

I have a big birthday party every year with cupcakes, and since I know a lot of vegans I always make vegan cupcakes as well as egg-and-dairy cupcakes. For vegan frosting, I'm a big fan of a particular margarine brand, though it has a somewhat silly name: Earth Balance Vegan Buttery Sticks. I don't know if it's available nationally, though.

Margarine has some drawbacks: It tends to be dyed yellow, which means if you make plain, uncolored frosting it will be an odd shade. Some margarines taste, well, margarine-y. If this bothers you, stick to chocolate or other highly flavored frostings!

we use Cherrybrook Kitchen mixes to make cakes and pancakes for our daughter who's allergic to milk and eggs. They are pretty good.
http://www.cherrybrookkitchen.com/products/index.php

There's an amazing cake recipe in Vegan with a Vengeance. Chocolate-Raspberry Blackout Cake... I make it so often, it's delicious. http://www.recipezaar.com/Vegan-Raspberry-Blackout-Cake-With-Ganache-Y-Frosting-166668

And if you go the cupcake route, Vegan Cupcakes Take Over the World is also a good book to take a look at. I made the banana split cupcakes for my boyfriend's birthday. So good.

crazy cake! my mum used to make this all the time when i was a kid. it's actually vegan... uses cocoa powder, but not actual chocolate, so there's no dairy. a quick google search provides many hits, but they're all basically the same, try nestle's recipe here: http://www.verybestbaking.com/recipes/detail.aspx?ID=136980
it's all made in the pan you bake it in, so there's very little to clean up (my sister often makes it while she's camping!). instead of frosting, this recipe just uses powdered sugar as a topping, but my mum used cinnamon and sugar which gave a delicate, almost crispy, top. SO GOOD! i've actually been craving it lately. it's light and moist and not too sweet. yum.

my gut instinct? Make a brownie recipe substituting canola oil for melted butter and use dairy free chocolate.

Maybe it's bias, but I'm usually suspicious of vegan dessert recipes. There are too many limitations (no eggs, dairy, and frequently no white flour) to taste like a traditional dessert. Since your friend can eat eggs, just not milk products, a simple substitution is likely your best bet.

And don't fret over frosting... not all desserts need it ;-) Simple coconut or nuts on top usually will suffice.

Oh, you could also serve a rich pudding made from (full fat) coconut milk, saffron, and pistachios...

Just to let y'all know (and I know this is an OLD thread): margarine is NOT dairy-free. If you read the label on just about any box of margarine (I have checked Fleischman's and "I can't believe it's not butter" as well as a few others), you can see that they all contain whey.