No doubt part of my affection for T.O.S. is nostalgic; I was one of those kids who grew up watching the Saturday morning reruns. But there are plenty of shows that I watched as a child which you couldn't pay me to sit through now... Star Trek isn't one of them. It saddens me that many newer fans of Star Trek have never seen an episode of T.O.S., and seem to find even the idea of it ridiculous. I think this is at least partially because T.O.S. has been around for so long that it has been parodied (often very humorously) countless times. Many people, I suspect, never get beyond laughing at the caricatures to objectively view the actual show.
Star Trek: T.O.S. isn't a perfect show by any means; it is frequently cheesy, and often gets invaded by '60's sensibilities and silliness- and there are some really bad episodes. But there are also a lot of really good ones: statistically more, I think, than most other Trek shows, which had seven seasons rather than three. Except for Enterprise, of course: they put that show out of our misery after four seasons, and there isn't one episode of that I would rather watch than T.O.S., even at it's worst.
So, if you're a fan of the later Star Trek shows or movies, or just of science fiction in general, I would recommend giving T.O.S. a chance. It might be an idea to ease in by checking out a top ten episode list and watching those first... you may be surprised by just how good it can be.