I saw my first episode at age six. It was "The Lights of Zetar," in first run. When the woman lying on the floor started gurgling and her face started glowing (it was a b&w TV), and then she died, I found it very scary. I did not like STAR TREK that night. I don't think I watched it again for several years. (As an adult I love that ep, oddly enough.)
"The Trouble with Tribbles" would be a great one, though.