What makes this a cult show?

For a me a cult show is a program that was popular enough in its time but sometimes ignored or dismissed when discussing quality shows. These shows are usually under rewarded too and have a timeless quality. This isn't to say that these shows "age" perfectly but they have
heartwarming or memorable characters that you can grow with, a good balance of drama and comedy, strong acting, maybe some cheesiness depending on the genre, and they stand out in their genre whether it's for the originality or fresh take on a popular genre. My favorite cult shows are Buffy, Gilmore Girls, and the soon to be considered cult show Bates Motel.

"When life gives you lemons"
Jessica D: sleep with their fathers and have secret lemon children 

I don't think you can predict at the time when a show is going to become a cult show. The original "Star Trek" only ran 4 years and was not very popular, and now 50 years later the franchise is still running strong. The same can be said of the original "Dark Shadows." Now with Netflix and On Demand, there are constantly new viewers for GG, so I'm not at all surprised that 9 years after the series ended, there's a strong fan base and a new GG mini-series. And yes, I do think quirkiness plays a part in it, or a better way of putting it would be creativity and originality.

It's fun no matter how old you are. I watched it when it first aired, when I was 13. Rewatched it in my late teens, and now in my late 20s. Obviously I related with Rory when I was a kid, and now I find Lorelai's stories more interesting. (What's next though, sympathising with Emily - remains to be seen :D)