My Dad was a big STAR TREK fan so we always had it on in the house when I was a wee lad. The one episode that was forever burned into my mind was "Operation: Annihilate!" The crew set down on a planet that was inhabited by these flying pancake like parasites that would attach to your spine. They would stick to the walls and for some reason be immune to phazers.
As a kid who already was freaked out by leeches, this was a terrifying thought. Even if poorly executed, just the thought of one of those floating by and clinging to your back was traumatic.
Apparently, as we learn from Dr. McCoy, they would inject tissue into your back and some how "meld" with you so that if it was torn off, you'd be killed along with it.
Fortunately this paved the way for my first viewing of ALIEN to be almost something that was passé! Well, not really.
I recently saw that episode for the first time (on the DVD set), but some shots were very very familiar to me…Then I realized they had been featured in the ads for the VHS releases of the show that played constantly on cable in the early 90s.
My biggest Trek trauma was from the Next Generation episode where there are big alien beetles that crawl into your mouth and possess you (at least I think I'm remembering that right). Somehow that grossed me out way more than the ear eels that did the same thing in Star Trek II.