One of the most memorable quotes from Gilmore Girls has got to be 'Oy with the poodles already!" which I have seen on many Gilmore Girl's paraphernalia that quote. I've seen mugs, t-shirts, mouse pads, you name it with that on it.
Another memorable one is 'Babette ate oatmeal', which originated from Kirk's plan to make t-shirts with things that happened in the town.
I mostly remember quoting 'copper boom!' with Hannah on the bus. Neither of us could remember what 'copper boom!' was from in Gilmore Girls, so I looked it up and found that it means quickly. So we used that for a week and then it died out.
Mom and I once were talking about Lorelei whining to Rory about how she couldn't write the reference letter for Luke in the 7th season. She said that she tried to write down what she was thinking and got a lot of scary gibberish that ended with 'Monkey monkey underpants', so I say that sometimes to Mom.