It depends on how badly the fins were damaged, the type of fish, age of fish (whether it is still getting significantly bigger or about adult sized already) as well as how long the fins were injured.  Additionally the quality of the water impacts things as well.  If a fish has had a fungus or bacterial probably that destroyed the fins or it was attacked by another fish that shredded them BUT it was very young it will likely grow back to some degree as long as you keep the water changes frequenty to keep the water clean. 

It the fish was adult sized when the injury occurs the healing can be very slow and will likely not be complete.  If the quality of the water is poor there will likely be little to no regrowth in many cases.