How long have you got??

I shall come back to this if I can think of the definitive ep!

Not a specific episode, but there seemed to be a number like this:

Wesley is doing his homework (inventing a Nuclear Reactor the size of a credit card), the Enterprise gets into peril, everything goes wrong, all the adult staff members are unexplainably rendered stupid, Wesley and his groundbreaking invention save the day.

I think this is fairly easy - but it will have to be one per series...

Original Series - Spock's Brain (the title says it all really)
Next Gen - Justice (happy world with lots of young fit people in very skimpy outfits who run everywhere and jump into the bushes with each other at the drop of a hat - need I say more?)
DS9 - Profit and Lace (Quark becomes a female)
Voyager - can I nominate all of it? No? Ok then, just Threshold (in which Paris and Janeway travel at warp speed and evolve into salamanders...)
Enterprise - Unexpected (in which the male first officer gets pregnant)

And of course, Star Trek V: The Final Frontier - uggh!