As a child, I was vaguely aware of something which I thought was called "Star Track", and I imagined it to be about a strange train that followed a track through the stars. I didn't like the series on the basis of this idea. (though in retrospect it sounds amazing). All of that changed when my father got me the computer game Star Trek: 25th Anniversary. The game got me interested in the setting, which set me up perfectly for when my brother came over and showed me Star Trek II: The Wrath of Khan.
After that, I watched the rest of the TOS movies in order, as much as possible. On my mother's suggestion I looked for a Star Trek TV series and found a random episode of Voyager. I was confused by that, as it had few ties to the Star Trek I knew (TOS). But I soon got into TNG by watching Generations. After I developed a habit of watching TNG, I tried Voyager again, catching the end of the first episode. From then on, I went to my friend's house every Wednesday for the new episode of Voyager. I discovered DS9 because it came on after TNG at night, at a time when I was dying for more Star Trek.
I like Enterprise a lot, too, although to me it's not half as good as Voyager (still one of my favorite series) or TNG. Nonetheless, I'm still disappointed it was cancelled. True, it opened the door for Star Trek (2009), which was great, but it's just really lame to me that there's no Star Trek TV series to watch. So instead I read the novels, the comics, and play Star Trek Online.