I was born in '59, so the turmoil of the 60's seemed rather remote to me also, I was mostly shielded from it, and it was still a time of relative innocence for me.
As such, ST hit TV when I was in the 6 - 10 year old range. So I watched it and liked it a lot, but to be honest(I know it's sacrelidge around here) but at that young age, I preferred Lost in Space. Mainly because I identified with Will Robinson. Not that I was anything like him, but because his character was living out my fantasy, exploring space and had his own "pet" robot.
Then in the early 70's, when I was in Junior High, a friend lent me two amazing books:
Stephen Whitfield's "The Making of Star Trek", and David Gerrolds "The World of Star Trek". This coincided with our local UHF station running the ST reruns every afternoon after school.
When I read those books, it created a new appreciation and fascination for ST. It was then that I realized that ST was more than the cool aliens and cool spaceships and the guy with the pointed ears that I remembered from childhood. GR had created a whole new universe and filled it with exciting adventurous people, and it was "about" something.
So I started watching the reruns religously, reading about episodes in the book and then watching them on TV. It was then that I became a "Trekkie".
Because I was mostly a dorky little geek in the 7th grade(and that was long before "geek" was cool) I felt that ST gave me something to feel a part of. I was very much like the kid in Galaxy Quest who pretended it was real, and fans were almost "undercover" Starfleet investigating the past. I know it was stupid but it was a way to handle all the harassment I used to get from the "cool" people and the jocks. My best friend was also a Trekkie, and when one of the bullies would make fun of us, he would hold up his Bowmar Brain calculator and scan it over the offender like it was a tricorder, and say, "No intelligent life forms present, Captain." Somehow that made it fun to be a Trekkie, to feel like we were a part of something special.
I've been a Trekker(the preferred term now) since then.
The amazing thing is how well that show holds up against all the modern shows. Unlike many shows, it's not dated. It's entertaining, exciting, sometimes funny, usually powerful in its statements(without being preachy like TNG could be), and just plain fun to watch. I never get tired of it.
Great thread, and great posts!