According to Wikipedia and various other sources, "Anatidaephobia" is an irrational fear that a duck is watching you.

It is not a real phobia. It comes from Gary Larson's The Far Side.

Anatidaephobia is pronounced as "an-uh-ti-day-uh-foh-bee-uh." It is the fear that somewhere, somehow, a duck is watching you.

Anatidaephobia: The fear that somewhere, somehow, a duck is watching you. This answer was found in The Farside Gallery 4, by Gary Larson, page 61, lower right.

I'm experiencing it right now, so that makes... one.

The fear of someone watching you is called Anatidaephobia.