Here is a classic:

Betty Crocker's 1956 Variety (very rich) Buttercream Frosting

Blend together thoroughly, 1/3 cup softened butter and 3 cups powdered sugar.
Add 3 tbl cream and 1 and 1/2 tsp vanilla (use a traditional hand mixer for this stuff and scrape the bowl religiously. It will get lighter and lighter as you mix air into it.)

Hey Thanks pinkperson for starting this thread and thanks all others for posting your icing recipes.
I just started baking and have baked only twice till date.
Each time, I used a store bought icing but now I can make one at home