I don't think there is anything wrong with fanfiction in and of itself, but most of it sucks. Too many fanfic authors have their own agenda and misinterpret the intent of the origina piece or character, not to mention stoop to inserting their own May Sues into the story. And worse still, fanfiction usually has no future.
Most fanfiction bores me to death, but I sometimes like to read really bad porno fanficiton, if only for the laughter value.
I admit to having written fanfiction in the past. I wrote a story about the game Lemmings Chronicles, and one Tomb Raider piece. Both of these make me cringe with embarassment when I think back on them, but I realize they were both necessary to help me learn how to write.
Of recent stories that I've written, one may technically be called fanficiton, because it is also legally unpublishable. It is set in a world that is not mine (a role-playing setting), but revolves around characters that are mine. I guess this technically constitutes fan fiction, but of a variety that is certainly more commendable than that which just utilizes characters that have already been written.
If you're at all familiar with the Planescape setting, you can read it here:
http://www.fanfiction.net/s/1604844/1/
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"And lo, the beast looked upon the face of beauty. And beauty stayed his hand. And from that day on, he was as one dead."