If I see a recipe I like and it includes a marinade or sauce where butter or oil is a significant ingredient, is there any way to substitute that fat and preserve a similar taste and texture? For example, I recently cooked a citrus shrimp recipe and simply skipped 90% of the recommended oil and it tasted pretty good, but I don't know what I may have missed out on. I know fat is pretty fundamental to food, so maybe the answer is no.
It depends entirely on the recipe and how it will be used. Fat can work as a medium for flavors and heat, to provide texture (especially in the case of emulsification), and for its own flavor. Blindly removing it from a recipe may "work", but leave you with something quite different from what was originally intended - whether that's ok with you is a personal decision.
Rather than looking to eliminate fat, look to maximize your benefit from it. Find out what purpose it serves in a given recipe, then find an oil you like that fulfills that purpose and add only as much as is necessary.
To add to what @Knives said -- it also affects texture and moisture in baking.
It's also important to remember that butter has water in it, so removing butter from a baked good might remove water vapor that's needed for lift -- and you can't just add water back in or it'll mix with the flour.
All that being said, in quick breads you can get away with replacing about 1/2 of the oil with applesauce or mashed banana. You might need to experiment to figure out how far you can get away with it. (and remember to write down what you did! I'm still kicking myself for the time when the low-fat apple/carrot muffins came out perfect and I have no idea what I did).
This will not work for other baked goods, such as those where you have to cream the butter first.
Oh ... and when you see butter being stirred into a sauce right at the end ("mounting" the sauce ) -- it's actually being used as a thickener, which will affect mouth feel. You might be able to use a starch to thicken it slightly, but won't have the same feel.
I think it is more important to look for what fats are in your ingredients. You should avoid transfats (mostly in prepared foods) and saturated fats, but unsaturated fats are very important for your health. See also this website as an example were to find information about this.
Oils and butters are very natural products. Skipping oil, butter, etc won't make your food healthier.
The rule of a thumb is to use fresh, natural ingredients: natural oil like olive, butter that has no animal fat added and made of non-skim milk. Those products will do you no harm, enrich the flavor of your food and (assuming you have a healthy lifestyle) make your body stronger.