Sometimes I cut the chicken up before cooking:
1) Cut off the breasts and pound flat and very thin with a meat tenderizer. Sear briefly on either side, then remove and sprinkle with walnuts, hazelnuts, herbs, whatever. Roll them up and place in a casserole, covered with tomato sauce or thinly sliced lemon, and bake for 20 minutes in a moderate oven. Serve with a salad and crusty bread. This might be one of my favorite meals.
2) Remove the legs. Dry them, dust with flour, and brown in plenty of fat in a wide hot skillet. Set aside the legs in a warm place, deglaze the pan with stock or white wine or both. Reduce the liquid by half, then return the legs to the pan, add whatever seasonings you want, cover and simmer for 30 minutes. You can thicken the sauce with more flour before covering if you want, but it's good to give it a stir or two during the final cooking if you do. Also goes nicely with a green salad and crusty bread, oddly enough.
3) Boil the remainder of the carcass. Strain and reserve the liquid. Pick off the rest of the meat. Feed the neck to the dog.

Make the cooking liquid into a gravy. Mix a bit of the gravy in with the chicken scraps. Fill flour or corn tortillas with the chicken mixture, as well as beans and cheese, roasted peppers, other veggies, whatever. Place rolled up tortillas in a casserole, cover with the rest of the gravy (adding chilies if you're going for enchaladas), maybe top with more cheese, and bake in a moderate oven for 20 minutes. Can also rip up the tortillas and make layers of ingredients, similar to a lasagna.
4) Break apart the major bones of the carcass and boil everything again. Soup? Stock for beans? I've nearly always got some kind of stock going on the back of the stove. Makes every other dish that much more delicious and nutritious.
That's all I got, y'all did the rest! Great thread for ideas.