For baking muffins and breads, you can try applesauce, but you may notice a different in texture.

If trans fats are the source you are trying to replace, then consider these alternatives:

Canola oil, Sesame Oil, Sunflower, Safflower, Olive Oil, Flax Seed Oil, and Coconut Oil

There are also new products available on the market that are trans fat free, such as Enova Oil.

Promise makes 0 trans fat spread (or at least it's 0.07% trans fat free, according to their advertisement).

Surprisingly, butter is good for you, and doesn't contain trans fats.

It all depends on your reasoning for wanting to eliminate or substitute fats from your recipes.