What are the best exercises to firm up loose skin?

Exercise wont help: Loose skin that is typically present after pregnancy or weight loss typically doesn't respond to exercise. Depending on the severity of it there are some.

No such thing: There are no exercises to firm up loose skin. Sorry! the only way this might work is by increasing the size of the underlying muscles so much that the skin tightens around the larger muscles. This is rarely desirable. Perhaps female arms or a male chest might be improved this way on occasion, but for thighs or abdomen, very few people want to make these areas bigger so that the skin is not loose.