Our system for making vegetable broth for soups and stews is the following. Whenever we're cutting vegetables, we add the odds and ends to a gallon-sized ziplock baggie in the freezer (our "broth bag"). When the gallon-sized bag is completely full, it's time to make broth, whether we have a soup in mind for dinner or not (the broth freezes well).
What goes in the broth bag?
Carrot tops, celery leaves, the tough outer layer of onion between the skin and the first tender layer, pepper seeds (jalapeno, bell, whatever), green onion tops; basically any part of vegetable that you wouldn't eat straight but is still edible.
The most special, not-so-secret ingredient in our broth bag is roasted green chile skins and seeds. In New Mexico, it's culinary custom to buy a large bag of green chile when they're in season (late August-September), and have them roasted on the spot. We freeze our roasted chiles with the skin still on (some people peel them all at once before freezing). Whenever we want green chile in our eggs, stew, burritos, etc., we defrost a baggie of green chile and peel the skins off. The skins and seeds go in the broth bag. Yes, this means every single soup of ours is at least slightly spicy! We don't mind.
What doesn't go in the broth bag?
I wouldn't put stuff that's dirty or gone bad into the broth bag. The thing about the broth bag is that it gets extensively boiled, so that should kill bacteria, but food that's gone bad might still taste off. Keep in mind that any pesticides or inorganic contaminants on the surface of the vegetable will still make it into the broth, so the vegetables that go in there should be washed just as thoroughly as the parts you eat straight away.
We boil the vegetable bits 'n' pieces in a few quarts of water for at least an hour, usually longer (if it's winter, we'll leave it on the woodburning stove for 3 hours or more). If we don't have that long, an hour in the pressure cooker is great. You can add bay leaves and other spices if you so desire, and definitely salt to taste. Strain the liquid and use right away or freeze.