This article is from the Fat-free Diet FAQ, by firstname.lastname@example.org (Michelle Dick) with numerous contributions by others.
The most common technique is to use fruit purees (apple sauce,
apple butter, mashed bananas, pureed prunes (some like to use baby
food prunes), etc) or nonfat dairy products (fatfree sour cream,
fatfree cream cheese, etc) in place of the fat in the recipe.
Substitution is typically 1 for 1 (I.e. 1 cup applesauce for each
cup oil). Many find that a better product is obtained by diluting
the substitute with water rather than using it full strength. When
using fruit purees you will also generally need to decrease the
sugar. Note that the fatfree product will be noticeably different
than the fatted version.