Okay, first things first: all great soup must start out with a great stock or broth.  This is my favorite stock recipe.  I find it's best to make a big batch of stock on the weekend, then freeze it in small quantities for later.  I freeze some in ice cube trays for when I make rice, and freeze the rest in quart containers.  If you don't have room to freeze all this, you can refrigerate the broth for 5 days without it spoiling.  To keep it longer, just bring it to a simmer on top of the stove for 10 minutes, let it cool, then refrigerate it for up to another 5 days.  You can repeat this process indefinitely.
**By the way, there is a difference between stock and broth.  Basically, stocks are made with the more "inedible" parts of the animal, like the bones.  This releases a high concentration of gelatin into the stock, which means that if you've made it right, it should turn into a meat jell-o in your fridge.  Sounds gross, but that means you have made one tasty stock!!  The author of my stock recipe refers to it as broth, but according to most definitions, it's actually a stock, so that's what I call it!

6 lbs. chicken backs, necks, or bones
1 medium-size onion, coarsely chopped
2 medium-size carrots, coarsely chopped
1 celery rib, chopped
4 1/2 quarts cold water, or enough to cover
1 medium bunch parsley
1 whole bay leaf
10 thyme stems
1 bouillon cube

You'll also need an 8-10 quart pot.

Preheat the oven to 450 degrees. Trim extra fat off the chicken parts and spread them in a heavy-bottomed roasting pan or large skillet with the chopped vegetables. Roast them until they are well browned, usually 45 minutes to an hour. Do not let the bottom of the roasting pan burn.
Remove the roasting pan from the oven, transfer the chicken and vegetables to an 8-10 quart pot, and pour off or ladle off any grease in the bottom of the roasting pan. Discard the grease. Pour 2 cups of water into the roasting pan and scrape the bottom with a wooden spoon to dissolve the juices adhering to the bottom. Reserve.
Add the parsley, thyme, bay leaf, and bouillon cube to the pot with the chicken and vegetables and pour the contents of the roasting pan into the pot. Add the rest of the water or slightly more or less if necessary to barely cover the chicken parts. 
Heat over medium heat until the water comes to a simmer. Turn the heat down low enough to keep the broth at a slow simmer and cook for at least 3 hours (I like to live dangerously and let mine simmer overnight).  If you feel like it, you can skim off the fat and froth that rises to the top every 30 minutes, but it's really not necessary.
 
When the broth is done, strain it into a clean pot or heat-resistant plastic container. Let it cool, uncovered, for an hour before putting it into the refrigerator. The next day, when the broth is cold, spoon off and discard any fat that has congealed on its surface. Pour into containers to freeze.