Um, well, I … uh …
I was a member of the Mötley Crüe fan club.
What? I was young.
I’ve also sent an email to Bruce Campbell and received a short reply.
I wrote a fan letter to Henry Rollins once, and got back a hand-written postcard, and one or two newsletters from his publishing company after that.
I’ve written a couple e-mails to Snopes, and got answers, but those probably don’t count as fan letters. (And they didn’t correct one of the errors I pointed out.)
I remember around 1960, I was a member of the Huckleberry Hound Fan Club.
I think they sent me a Huckleberry Hound Fan Club Official Membership Card and a letter welcoming me to the club.
Pretty sure I’ve mentioned this before . . . In 1994 I wrote a letter to Billy Joel before a concert in Milwaukee, thanking him for writing my favorite song (“Vienna,” which was not one of his big hits, so he rarely played it live) and telling him how it helped me through hard times. At the concert, he mentioned the letter and then played My Song. W00t!
I also wrote a letter to Jean Merrill, author of The Pushcart War, telling her about how Mr. S and I discovered that we had both read it as kids, which helped pull us together as yet another weird thing we had in common. I sent a copy of the book along with it and asked if she would inscribe it for us. She did, very amusingly, and also enclosed a charming two-page letter with extra tidbits about the book. We had it framed, and it’s on display in the living room along with the book.
When I was in 3rd grade, we had a class assignment to write a fan letter. Everyone else wrote to heads of state, movie stars, sports heroes, etc. Some of the kids received signed photos, others never got a reply.
I have no idea why, but I wrote to the mayor of our small suburb. I think it was the only fan mail the guy ever got. For my unique effort, I got my picture taken with the mayor, and he gave me some kind of plaque. The picture and story appeared in the local paper, and I got my 15 minutes of fame.
Before the end of his term, the mayor was kicked out of office, for being the crookedest politician in memory.
The only fan letter I’ve ever written was in high school, to Michael J. Fox. I had a huge crush on him, and I still have my MJF scrapbook. 
I got back a “signed” postcard of him in his Light of Day getup.
The only fan club I’ve ever joined was in college, for the band Too Much Joy. I got a t-shirt and a button and maybe a sticker, I don’t remember anymore. I was a big fan for about a year, until I went to a live show and tried to say “hi” to the guys as they passed (it was a very small venue) and they totally blew me off, plus they were all kind of scowling. That made me decide that they didn’t give a shit about their fans, and I stopped being one. But I still listen to Mutiny from time to time.
I almost wrote a fan letter to author P.D. James not too long ago, but her web site makes it clear that she hardly ever reads, let alone responds, to them. I don’t think I’d ever write to someone famous expecting a response, but knowing that I won’t get one makes it somehow not worth the effort.