hrm... I know from Petsmart that they can make your dog really sick...   Oh no wait.. those are tapeworms..   nm..

There are 20,000 species and only a few are harmful.  most of them eat detritus.  But its hard to identify the bad ones so we pretty much have to eliminate flatworms in our reef tanks.
There is a product called 'Flatworm Exit" but its recommended that you remove as many as you can before treating the tank.  If you treat first, then you have a ton of flatworms dying and hurting water conditions. You can suck them out with a regular air hose.
A sixline wrasse would gobble them up too.
For the most part they are harmful, but not pretty once they grow in numbers

flat worms are not all bad in fact only a small number of species are harmful the problem is distinguishing the good from the bad so we must eradicate them all

that sure is gross

I definitely dont have an infestation likethe above pic but there are a few.  usually on the front glass.  in the last couple months i have not noticed their numbers getting out of control