Not alot of recipes call for it. If you're making sauces, clarified butter is always preferred for the roux. If you're making an omelette or any other frying application, then clarified butter is used because it has a high smoke point.
The only other application I can think of offhand is brown butter blondies, a recipe in Williams Sonoma Essentials of Baking. (great book, by the way) It's sort of a cross between a brownie and a shortbread. It's a nice simple everyday recipe that will please just about everyone.
1 1/2 cups (7 1/2 oz) ap flour
1 tsp baking powder
1/2 tsp salt
2/3 cup (5 oz) clarified unsalted butter
1 cup (7 oz) packed brown sugar
1/2 cup (4 oz) granulated sugar
2 large eggs
2 tsp vanilla
1 TBSP lemon juice
1. Butter an 8 inch square baking pan. Preheat oven to 325.
2. Sift together dry ingredients, set aside.
3. Brown the clarified butter in a frying pan over low heat until fragrant, about 6 minutes. Let cool slightly.
4. Combine brown butter, sugars and stir with wooden spoon in a large bowl. Mix in eggs, vanilla and lemon juice until smooth. Stir in dry ingredients just until incorporated.
5. Scrape batter into pan and spread evenly. Bake 35-45 minutes or until toothpick comes out clean. Transfer to wire rack and cool.