You'll notice that there are several opinions presented for some of these substitutions. We recommend that you experiment yourself. Comments with your experiences are welcome!
butter or shortening
use half peanut butter in chocolate chip cookies or other cookies you'd like a peanut butter flavor
3 tablespoons flax seed meal per 1 tablespoon fat or oil
use applesauce in equal amount plus a little flour (check for consistency)
use pumpkin in equal amount for cookies, breads, muffins, etc.
applesauce to replace part or all of the oil in cakes, muffins, cookies, etc. May change flavor slightly. Another sister told us that this substitution gives a spongy/rubbery consistency and muffins stick to the papers. She recommended using half oil, half applesauce.
pumpkin to replace all oil in baked goods, or up to half
use applesauce to substitute for up to half of the amount of oil in a baking recipe
use light olive oil (not extra virgin)
pumpkin in equal amount
cooked, mashed white beans work with up to half the shortening replaced with beans. Experiment to replace an increased amount.