What are this worms

[Elio]

What are these worms in the video? Can they be harmful to Goldfish or other small fish?

They don't look like planaria or detritus worms to me.

Thanks for your help.

Elio.

[DaveO]

Leech

[Guppysnail]

I cannot blow the video up enough to see (bad eyes)distinguishable characteristics. Three things about the locomotion make me think leech as @DaveO said. Inchworm movement. Shapechange with extensions and contraction and strong S swimming motion. Start with aquarium leech on a google search to see if you can identify it. 

Most are not harmful fish will eat them but a few could pose issue. Most common are the non harmful that live off  micro algae/bacteria. 

[Struggle]

Looks like a leach to me and if your fish are big enough they’ll eat them.

[Biotope Biologist]

That’s a leech as others have pointed out. You can make out the circular posterior disc that it uses to suction to things to lie wait. Goldfish often enjoy eating them.

if the goldfish are in a pond it’s likely a local transplant.