One or two chicken livers, along with gizzard and heart, are perfect for a light breakfast fried in butter or rendered chicken fat with onions and eaten with buttered toast. The organ meats generally are more nutritious than the regular muscle meat. Ironic, considering their status in this culture...
Feet are excellent in stock. If you're making stock without the feet, you're missing out. They contain a lot of gelatin-making potential for a higher quality stock. Heads are nice for stock too (cleaned of feathers and rinsed well, of course). Necks are good in stock too obviously... After roasts and such, all bones, gristle, uneaten skin, etc. go into making stock. After making stock, the solids go into the scratching yard, where the flock pick the bones clean and the bones are eventually composted.
If we slaughter a fat old hen, we save the fat from inside the belly to render along with any other fatty trimmings (these can be saved in the freezer till you have enough to render a decent quantity at once). You can eat the cracklings too. It's not as good as lard, but still tasty and useful (not good for high-heat though).
Blood can be collected and made into sangette or similar (this is a kind of "blood omelet" for lack of a better description, a traditional French peasant dish). I like making a kind of sangette with garlic and onion, fresh parsley, and salt and pepper, and eat it for lunch with buttered toast. It's better than it might sound, actually... If you enjoy blood sausage, you'll love sangette!
We don't use the feathers for pillows etc, because we scald to pluck... But we do compost them so they wind up as fertilizer indirectly.
We compost remaining innards, but if I had a pig I'd feed them to it. They'd eat anything but the feathers (and probably eat a few of those too).
Waste not, want not (and show respect).