I cook them in a crock pot until the meat comes easily off the bones. Take out the meat, remove the bones, and use the meat in burritos, chimichangas, enchiladas, tacos, tamales, BBQ sandwiches, casseroles, stir fry, pasta dishes, chicken salad, or whatever dish in which you'd use cooked meat. Sometimes I even make chicken and dumplings, or soup. Recently, I made some chicken-dip sandwiches, just like a French dip, only with chicken, and chicken broth for the au jus. It was delicious.
I use all the meat, even from the necks and backs. Once it's chopped up, if it was stringy, it's not noticeable.
Any broth remaining after the meat's gone, I freeze and save for stuffing, gravies, or anything else that might call for stock. Broth from older birds is amazing, dark and rich. Looks almost like beef broth.
You might also look up the recipe for Coq au Vin. I've never made it myself, but several folks on BYC have tried it, and gave it rave reviews.