I adore Ina Garten's Coconut Cake (and the same in cupcake form), and the frosting is also a favourite in our house:

http://www.foodnetwork.com/recipes/ina-garten/coconut-cupcakes-recipe/index.html
http://www.foodnetwork.com/recipes/ina-garten/coconut-cake-recipe/index.html

Just omit the coconut, of course.

here is a good chocolate frosting recipe

the original recipe did call for an egg, but i left it out and the frosting was absolutely delicious without it. you could also modify to use milk chocolate, dark chocolate, or white chocolate, whichever you prefer

Ah yes, the magnolia buttercream recipe... otherwise known as the recipe on the back of the 10x sugar box ;)

A boiled milk frosting, sometimes called Miracle Frosting, would work for your cake. It's a delicious frosting that is stable at room temperature. It's creamy, fluffy, and lightly sweet without eggs or shortening. I've used it to decorate red velvet cake and emon cupcakes.

http://www.treats-sf.com/2010/12/miracle-frosting.html

1 stick butter
1 lb confectioner’s sugar
1 tsp vanilla
1/4 cup milk

sets up nicely and you can definitely decorate with it!

MAKE THIS FROSTING!! My sister gave me this recipe and I use it on everything! It's very light and not overly sweet.

3 cups of whipping cream
1 large box of instant vanilla pudding

Stir together whipping cream and vanilla pudding then whip with a mixer until it's stiff (but do not over beat). That's it! I've added a little bit of caramel to make caramel frosting and I've added Bailey's to make an Irish creme frosting...seriously amazing and SO easy!

I like this chocolate frosting from Martha Stewart:

http://www.marthastewart.com/318370/mrs-milmans-chocolate-frosting

But, I've used just chopped dark chocolate & whipping cream and it turns out rich and intense and dense. Let it set up in the frig before using.

I've done what Kort suggested, but also substituted cream cheese for the butter. It's a little softer, but still very tasty.

I like an old-fashioned buttercream frosting (or at least that's how I think of it!) I used it on this coconut cake with blackberry mousse.

THe secret is in the whisking!! It comes out amazingly thick and creamy. And you can add any flavorings you like. I added framboise, but vanilla's always a good choice.

Smitten Kitchen has an awesome birthday cake and sour cream frosting.

I'm a fan of the frosting used in this cake recipe: http://www.thekitchn.com/recipe-weeknight-layer-cake-bu-80097

I second (third?) the cream cheese frosting. I also love the Hershey's Cocoa Powder box frosting recipe for chocolate frosting. I don't think it has any of those things.

I love cream cheese frosting, however, I don't like super sweet stuff so I usually halve the sugar amount and it always works like a charm. Also, I scape a vanilla bean and mix the seeds with the sugar before I make the icing.
Alternatively if I want a somewhat light 'frosting' what I do is make a batch of whipped cream and cover the cake with it at the last minute.

Confectionary sugar
Heavy Cream
Vanilla or other flavoring of your choice
food coloring if desired

Whip heavy cream and sugar until frosting-like consistency. Add seasonings and colorings to taste.

Dead simple, dead easy, impossible to screw up.

I love how butter + icing sugar + milk + vanilla (add some food colouring if you want) is referred to as Magnolia Bakery's recipe- to me that's just icing as families across Australia have made for years upon years.

Butter + icing sugar + milk + vanilla is always a winner. Try mix butter first, then add some icing sugar and tablespoon of milk and mix. Then you add as much sugar as you want to.

I usually taste so often my frosting that I need a break before eating a cupcake or whatever I baked hehe

You can also add cocoa powder if you want to turn it into chocolate frosting.

also, a great peanut butter frosting, or you could omit the peanut butter and keep it vanilla (or any other flavor by adding corresponding extract)

If you want a calarie free frosting...try Cool Whip Free. I use it all the time.

Sorry Calorie Free

I have a super-easy, super-quick, buttercream hack. And, by buttercream, I mean gorgeous, white, delicious not sweet buttercream which pipes beautifully and is a shockingly simple version of Italian Meringue buttercream.

Faux Italian Buttercream

3 1/2 Cups Marshmallow Fluff (basically, 1 jar)
5 sticks of unsalted butter (yes 5!!)
2 1/2 cups of sifted powdered sugar (I use less -- 1 1/2 - 2 cups)
1 tbsp clear vanilla*
Pinch of salt

In a mixer, blend together marshmallow fluff and butter until creamy.
Slowly mix in the powdered sugar.
Dissolve the pinch of salt into the vanilla, then slowly mix in.
Blend until well mixed and fluffy.

Will make approx. 6 cups of frosting, enough for 4 dozen cupcakes.

*You may use regular vanilla, the frosting color will just be off white.

http://ovenofdreams.com/?p=10

Mascarpone cheese, confectioner's sugar, heavy cream.
YUM.
I've had great success with the version in Martha Stewart's Baking Handbook.

Not sure if this meets your criteria, there is no eggs, but there is butter. Tasty kitchen: "That's the best frosting I've ever had" recipe. Link below.

http://tastykitchen.com/recipes/desserts/thate28099s-the-best-frosting-ie28099ve-ever-had/