I was never really a fan of the original series. I like the characters but I have a hard time getting into a show that is so old.
I have seen every episode of The Next Generation, and most of Voyager and Enterprise. I just started watching DS9 for the first time.
TNG brought me into trek, and after that its successors. I could never manage to look at more than a few episodes of TOS consecutively at the time. Because it was so old, the pacing so slow, the technology and story ideas so dull .
By this 'dullness', I mean that TNG took a lot of concepts from TOS, and expanded on them. Having seen those TNG and DS9 versions first, the concepts in TOS looked old hat and unimaginative, even though I rationally knew they were the originals. Perhaps that's the same as when people keep preferring the music that was popular when they were teenagers, because that was the music they heard first, the 'real music'. Even though they often learn later that most of those were really ripoffs of yet earlier music.
Also, at that time, I was mainly into Trek because of its philosophical concepts and its technology. My interest for character interaction -in which TOS definitely outshines TNG and VOY- only came later.
It has only been in recent years that I've begun to see that there is something unique in TOS that has mostly been lost by the later series. If I were to put it into words, it would be the sense of friendship between Kirk, McCoy and Spock, as well as the sense of really being on an adventure to explore the great unknown galaxy, guided by ethical guidelines (interpreted freely at the Captain's disgression) instead of a lot of stuffy, constricting rules and political correctness (TNG).
On an unrelated note, I recently watched some early DS9, it seems I had really forgotten how incredibly irritating Julian was in the beginning
Luckily, he grows to be much less so in later years