This post was the very first idea I came up in the 100 Things Fanfiction series. It's probably going to consist of a bunch of shout-outs to my friends, but that's okay. My friends are the awesome people who inspired it.
Writing fanfiction (and generally being involved in fandom) has allowed me to meet several people that I count among my closet friends. Some of them write fanfic, some don't. Usually, we've struck up friendships when they started commenting on one of my stories, although I think a couple of them were on a message board with me about 8 years ago.
Aruna7 and I met when I commented on one of her SG-1 fanvids (which I would link to but I don't think is online anymore. Little did I know that one innocent comment would lead to multiple ongoing collaborations and a friendship that (I hope) will be lifelong.
Lhinneill, Cha_aka, and I have roleplayed together, read and helped one another with our stories, and generally shared our lives for almost as long as I can remember. They're the first people I share anything I write with (except for One Path.) and the first people I think of when I'm stuck in a story.
Polgarawolf and I met through her comments on One Path, and since then we've probably exchanged enough commentary on Dune, Star Wars, and various other franchises to fill multiple books of analysis and criticism. She's been my sounding board through a lot of story-related problems, and my fridge is full of snarky magnets she's sent me as gifts.
There are other people I've gotten to know on a more limited basis through my fic writing, but who's input and insightful comments on my stories have been invaluable to me. Teddibear, Nrgbunny and Phantom-Jedi1 all stuck with me through epic-length stories, caught mistakes that even my betas missed, and inspired me to keep going when I might have given up. I can't mention everyone; the post would start to read like one of those genealogy lists from the book of Genesis.
What I've learned is that fan art means more when you can share it with others. Doing so will lead you to meet and make friends with people you might otherwise have never met.