Well given that we saved the world by WRITING fanfiction I'd say most of us have an opinion on it.

I'm actually surprised this topic hasn't come up sooner (it hasn't has it? We aren't just rehashing an old topic here, are we?)
It IS very much a victim of Sturgeon's Law, of course, but then what isn't? I have read some fantastic fanfiction that can easily rival professional original works. I think fanfiction is the way in which people continue their own experiences with a medium, engage with others, and explore the worlds created by others. Sometimes you get some really original imaginings out of it.
Of course other times that backfires... I remember hearing a very sad story about an author who was very willing to engage with her fans and appreciated and read fanfiction, until one day a fan totally coincidentally managed to produce a fan story that was VERY similar to the plot of a book she was currently writing. She contacted said fanficcer and mentioned this, offering a credit for the ideas in the book itself. The fan did... well she didn't react very well, and became very combative about it. Incidents like this explain a lot of authors really won't read fanfiction of their work, whether they accept it or not.
I think I'd like to create a universe people wanted to explore like that, although I might not agree with other peoples interpretations, it's really interesting to see HOW an audience's interpretation varies from that of the creator, and everyone engages with fiction in their own personal way. Everyone sees things the way they personally want to see them, and they usually view things according to their own perceptions, hence such tropes as 'Draco in Leather Pants' and 'Ron the Death Eater'. (Fitting that Harry Potter has one of the largest fanfic collections on what fanficcers refer to as "the pit".)