I have never in my life been tempted to send someone fan mail. Maybe because I'm just not the sort of person who is that interested in the lives of celebrities. In today's world, where authors you read even stop by your blog, where you can send personal messages to authors on Twitter and sometimes even have them follow you back, relationships like the one discussed here can never develop. That's kind of sad.
In a way, the world is more inclusive these days. Everyone can read and comment in online discussions, they're not limited to two participants. But there's something to be said for the exchange of lengthier correspondence, as well. The epigraph of my PhD dissertation is Darwin's "warm little pond" quote, which is particularly applicable to my doctoral research. This quote came out of a letter from Darwin to Joseph Hooker. People just don't send letters like this anymore. E-mails won't have that same staying power.
Hate mail, or rather disapproval mail, on the other hand, is something with which I'm acquainted. I was so angry over the re-election of George W. Bush in 2004 that I sent hand-written letters to the White House every week criticizing his policies. I ran out of steam after about six months, but I still have some of the replies in a 3-ring binder around here somewhere. (You don't get too many replies, honestly. And some of them are pretty generic.)
In the end, I guess it's all about what you're passionate about. Those who have sent fan letters did it to express genuine admiration, whereas I was only so inspired when I was angry.