I was just a bit too young to remember watching Trek when it was in first-run on television (but I was alive then, and it's certainly possible that I was present while the TV was on), but I vividly remember watching it in reruns in New York City, on channel 11 right at dinner time on weeknights (sandwiched around The Odd Couple and Beat the Clock, at least for a time). I don't know what it was about that show that struck a chord with me, but something definitely did, and I tried to never miss an episode. My parents didn't think anything of it, and happily indulged my passion with Star Trek toys, model kits, and action figures (back then we had the big 8" action figures, with uniforms made of real material, not just molded plastic, and removable phasers, communicators, tricorders, etc.). I had almost every one of those things you could get (in some cases more than one, and I would put the uniforms on other figures to beef up my team of red shirts to go down to the planet and get vaporized). I remember getting up extra early to watch the Animated Series once I discovered it, and being bewildered when I couldn't find it any more.
I had the earliest of the books; one of the first book reports I remember doing was on "Spock Must Die!" The old James Blish adaptations of the original Trek scripts were favorites, and I devoured "making of" books like "The Trouble with Tribbles ("the book on how to write for TV," as the subtitle claimed), "The World of Star Trek," and "The Making of Star Trek." I got several copies of the Star Fleet Technical Manual by Franz Joseph, and still have a rather large collection of 1st printings, for which I scour used bookstores when I have the opportunity. I have no idea if they're worth anything, but I like having them and other things, like the original Star Trek Maps, blueprints, and so forth.
In the aftermath of Star Wars, Trek became once more a hot property. Star Trek: The Motion Picture came out, and with it a slew of new novelizations. From the awfulness that was anything by Diane Duane to the ultimate coolness that was the John Ford Klingons, it was a great time to be a Trek fan. (Trekkie? Trekker? I didn't, and don't to this day, consider one cooler or more derogatory than the other.) Wrath of Khan followed, and things were rolling. A few friends in high school shared my passion, but not to the same extent as me, and it wasn't until college that I actually met others who were into Trek as much as I was. My best friend Bob and I took in our first Trek convention together that year in Boston, and I was in hog heaven. Bob had even written his own Trek novel, set on a ship other than the Enterprise (which at the time was a novelty), and even had insignia made up for the ship (I still have one, Bob, if you're reading this).
Over the years my love of Trek never diminished, and gradually turned into full-blown fandom. Conventions, uniforms, Trek-related games, fan clubs (I performed a wedding at a Shore Leave convention in Maryland, dressed as a Mirror Universe chaplain; "Let us prey... upon those who are weaker than ourselves..."). In fact, it was while in a Star Trek fan club that I met my wife*, and to this day some of my closest friends stem from those grand days of friendship and fellowship, built around our mutual obsession. Sure, I'm a fan of most if not all science fiction that comes down the pike, and Star Wars holds a place dear in my heart, Dr. Who is mostly great, but to this day I'll watch Star Trek if it's on in any form; whether it be one of the series (yes, I even like Star Trek Voyager), the movies, or even a special on a channel like Biography. My wife and I spent a great few months having our "can't miss together time" around watching Star Trek Deep Space Nine on DVD from start to finish.
Trek's made a lasting impression on my life, and made me some of the best friends I've had. And I don't think it's any odder than being able to quote baseball statistics or spending hundreds of dollars on football tickets.
* The first year we were married, we both tried to get the other a print of "New Borg City" for Christmas. Trouble is, the store only had one, and we were both trying to do it behind the other's back! It was a hoot once we and the guys at the store all realized what was going on.