no algae is not harmful for the fish.... but it is a sign that you may have too many nutrients in the water, overstocking, overfeeding, etc. As everyone else arlready said.
Sooo what to do about it? Yes you can check for phosphates and nitrates and if they are high this is probably the cause. Cut back on feeding, go up on your water changes, how often have you been doing water changes? I do mine at least once a week.
What size is your tank? What kind of lighting do you have?
You could always add some live plants!!! If you have low light you could start with low light plants- anubis, crypts, javer fern/moss.
What kind of fish do you have? If the tank is big enough you could always add a "clean up crew" Pleco, Otos...