I celebrated Star Trek's 45th anniversary last night by watching “Charlie X,” which I'm pretty sure was the first episode I saw in 1966. I found it by accident while flipping channels. Note that in 1966 our town only had one channel and, because we lived on a hill, we could get three to five out of town channels. There were only three networks anyway so flipping channels wasn't what you might think.
Of course I was a fan during it's original run though 1969. The first season was on Tuesday nights, the second on Thursday nights, and the last year it was on fairly late on Friday night, either 21:00 or 22:00 as I recall.
However, I became an even bigger fan when they started the reruns in 1970 or 71, when it was on every afternoon after school.