Many of the "fat free" diet products are also "nutrient free". When the fat free craze was popular in the 90's, there was fat free cookies/pudding/chocolate syrup/candy and everything was labeled FAT FREE!!!!! but it was still junk, and still loaded with sugar and empty calories.
There are good foods that are low fat/fat free-such as fruit, veggies, oatmeal, and skim milk...and then there are the fat free/low fat JUNK foods, which are just as bad as a full fat cookie/pudding. Actually, fake fat free foods are worse for you, because a fat free cookie or pudding digests much quicker than one with fat in it, and you actually end up hungrier sooner, and have cravings.
I think it is okay and healthy to reduce fats that you don't need-such as buying skinless chicken breast, over the higher calorie/fat chicken with skin on...or having foods that are naturally low fat like mentioned above-but fat free snacky things aren't good for you at all. (Regular Pepsi is fat free, for instance.
There is also a difference between fats:
fat in nuts=good
Not all fats are created equal.