Every Star Trek Reference In Futurama

The Episode The Day the Earth Stood Stupid bears some striking similarities to the Original Series Episode Operation - Annihilate!

The Futurama episode follows the attack of a species of hyper-intelligent brains attacking planet by planet, crossing the galaxy destroying civilisations, eventually attacking earth. The crew are tracking these destroyed planets before the brains arrive. The brains turn out to be a species intent on destroying all though on earth and it turns out that only Fry is immune to their powers of making everyone on the planet dumb. This is told to Leela by the Nibblonia council who have been fighting the brains since the dawn of time.

This is similar to the Star Trek episode, in which The Enterprise is tracking a series of planets whose residents have gone insane and destroyed their own civilisation. While the end result is not flying brains, it turns out each planet is being attacked by a species of single-celled organisms that are sending people insane.

The reference to Star Trek is clear in the episode, The brains and the organisms both do not physically damage thing, but by sending the inhabitants of each planet into abnormal mental states, insanity and sheer stupidity, they are able to destroy multiple planets in sequence from inside.