JKR's quotes about Fandom in 2008, mainly from Accio Quote and the Harry: A History website. The last two have different sources.

I had people as early as Prisoner of Azkaban, the third book. I remember a woman saying to me : "I think Snape loves Lily". I was "Oh my God what the hell did I give away ?". But so people, people got stuff very unnervingly right. Often. Yeah.
~ JKR interview on receiving the James Joyce Award

It’s very strange to think that you must have been pretty much the target audience, ten years ago, so you’ve really… you have been reading this book all through these ten years so you are… You are my people ! No, I don’t mean in any political way, I’m not trying to lead you to an uprise or something… Yes, it is odd to sit in this room and to think that Harry Potter would be examined in that particular way and in a room with people who are exactly the age that Harry was, really.
~ JKR interview on receiving the James Joyce Award

...it makes me enormously happy that people continue reading and enjoying the books. They grew older with Harry Potter. But I never thought adults were potential readers.
~ Interview in Spanish newspaper El Pais

...the other day I was on the street and a woman came up to me and asked if I was J. K. Rowling, I said yes. She then said: “You deserve everything you have.” I don’t think she was talking about the money...
~ Interview in Spanish newspaper El Pais

...it's not about love of a story or even wishing to spoil a story. It's become something that people want to be attached to because it's the quickest way they can see to get some publicity for themselves or notoriety for themselves and you have this fringe - I can't dignify them with the word fan because I think if it wasn't Harry Potter it would be Star Wars or it would be something high-profile enough that they could just get a little bit of face-time. ... it's really got nothing to do with Harry Potter...
~ JKR in Vault 27 on HAH 

... I'd become used to the fact that people were so invested in this world, and felt such ownership of this world that I was not on a pedestal at all in their eyes, I was right in the thick of the fight. And it's uncomfortable on and off the pedestal, so you get used to it."
~ JKR in Vault 27 on HAH

...if a fight comes to me, I will not duck it. So, if people want information on my characters, then they have to accept that I'm going to give them the information on the characters. And if they don't like it, that's the nature of fiction. You have to accept someone else's world because they made that world, so they probably know a little better than you do what goes on there.
~ JKR in Vault 27 on HAH

I was not at all new to the concept of fan entitlement because that had now been going on since, I think, around 1999. As the Snape Debate hotted up, I would occasionally receive mail from fans that was instructing me on my characters. And you know what, that's very endearing when it comes from a younger person, and it's less endearing when it comes from an older person.
~ JKR in Vault 27 on HAH

At no point have I indicated, or would indicate,  that any of these fan websites is a "favorite."
~ JKR Declaration for Trial, Feb. 2008

Welcome to Pottercast, your number one source for news, theories, discussion and interviews . . .  I know a small amount myself, having written the books. My name is J. K. Rowling. I am now happy to introduce your hosts: Melissa, John, and Sue...
~ JKR's weekly intro to Leaky Cauldron's Pottercast