I was trying to figure this out the other day.. we used to watch VOY's Future's End every time we were having movie night at home because it was more fun then most movies. I've seen it more times than my favorite VOY ep, Timeless. So there's the approximately 4 times all the way through VOY viewings and then the movie night events for Future's End. My favorite ENT ep, E2, I've only seen 4 times, during each ENT rewatch, never chose to watch it separately. This is what happens with eps that take place in a bigger story arc, I don't get around to watching them as stand alones. None of these eps are the winner though.
When I was a young teenager I was watching TOS twice a day, five days a week because I could get it on two different channels by skilful antennae twisting. I had a little notebook with the ep descriptions cut out of TV guide and pasted in, I would put a tick next to each ep as I watched it. The eps were shown randomly yet there was definitely a person choosing them. The ones considered great were shown far more frequently whereas there were eps like The Lights of Zetar which I only saw 3 times.
City on the Edge of Forever was the clear winner in the notebook with 13 or 14 viewings and since I've seen it at least 5 times since then it is the winner.
Cause & Effect (love a causality loop)
Surprisingly it's probably Where No One Has Gone Before from TNG. It's not like an episode that I love or anything, it just always happened to be on. The network that showed reruns of TNG would always start from Season 1, do a couple of seasons, and then inexplicably go back to the beginning. Whenever I'd catch it, that episode would usually be on. Stupid Traveler.
I've seen every single episode of every series the exact same number of times. I watch a series front start to finish every time.
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