"What's that?" you say, eyes aflame. "Are you promoting non-canon uses of others' works with no potential for profit involved?"
In spirit, and often in practice, there is absolutely nothing wrong with fan fiction. Nothing. Don't give me that look. Fan fiction is, without digging any deeper than the very surface, a great vessel for learning some of the finer points:consistent character voices, plot that adheres to the worldbuilding, voice. Things we need to develop as writers, if we wish to work in any sort of professional sense.
Now let's go one level deeper. I bet you can tell where I'm going: companion novels. The Star Wars expanded universe, Star Trek novels and stories, the Myst books--they're all fan fiction, and don't try to tell me they aren't. Here's the difference: they're able to be sold, and are (normally) considered a part of the canon. It's like the difference between a patented design and the same design without the fancy stamp. but, for whatever reason, that stamp makes people assume that this thing is okay, whereas anything without the stamp is pure crap.
One level deeper. The first year I went to SpoCon, I went to a panel. I have no idea what it was actually about anymore, but at some point the subject of mythology came up. All the panelists espoused what a great source of stories. And they are completely right. Then, maybe ten minutes later, the subject of fan fiction came up. Two of the three panelists, intelligent people, immediately called out fan fiction as wrong, since you weren't pulling the story from your own mind, but rather from an outside source.
The other panelist poked up her head and pointed out that taking material from mythology is the same exact principle. Those two nay-sayers shut up about the subject. That's the third level, here: nothing is new.
So, in less than polite terms, everyone needs to pull the stick out and realize that fan fiction isn't evil. It's actually quite good and, as much as anyone might wish to deny it, not that uncommon, when you start thinking about myth and legend.