Being a supporter of what would probably be considered as the most controversial ships in the series, from Harry/Hermione to Sirius/Remus to Snape/Hermione, I guess it's about time I weighed in on this discussion.
The impact of ships on the readers' vision of cannon (does it detract from it, add to the story, etc.).It certainly doesn't detract from it. I think it enhances it, adds a whole new dimension. At least for me. Ever since we were little, when my sister and I used to dress up and pretend to be Mary Poppins and Jane Banks, we used to make up stories about what happened to Bert, Mary, Jane and Michael later because we didn't want to believe that the children never saw Mary again. I did the same thing with many other films and books I've liked over the years (and, rather sadly, one or two video games too

) I think millions of people have probably made up stories that are continuations or extentions of canon plots and if anything, they enhance the enjoyment of the books/films. They lead to a greater understanding of the characters, if the fanfics/stories are written bearing canon characterisations in mind, of course. Which are the only sort that I really read...I don't like fanfics where the characters are completely off the wall because it just doesn't feel natural. I know that there are some who like that sort of thing, and great for them, but it's just not for me.
I think the greatest compliment I ever received about the fic I wrote was when a reader told me that after reading it, they really believed that it was possible for Snape to have a sister. That made my day, it really did, because I do try to keep my characters as canon as possible, whilst still having the freedom to expand on what JKR has created. Although obviously not canon, I would like to think that what I'd written complimented the series rather than detracting anything from it, providing an extra dimension for those who would like to know a little bit more about the adult characters than we are allowed to see in the books. I'm sure that's what most fanfic authors are aiming for.
The appropriateness of certain ships (i.e. Slash, Young/Old, etc.) in a series originally intended for children.I don't think this really needs to be an issue. Whilst the series is aimed at children, there's enough in there to keep adults interested too (though not as much as I first thought, but that's a whole other ballgame

) Adults need an outlet to explore their own ideas too, and there should be a place for them to do that. Obviously, adults will be interested in pushing things a little bit further than might be appropriate for children, but there's nothing wrong with that. Slash is no more inappropriate than real life homosexual relationships. Though it will never be canon, I've always supported Remus/Sirius, and I've read and thoroughly enjoyed Remus/Severus, Harry/Severus, Harry/Draco and Hermione/Bellatrix (rather racy, those ones

). Though I do have to admit, the more wild the couple, like that last one, the harder it is to find a trace of the original canon character! I think that there is a lot of scope for the Remus/Sirius ship whilst keeping the canon characters, and that's again what I tried to do with 'Completion'. I've read a lot of fics that also have very canon characters and still allow for the Slash ship. I don't think there's anything wrong with the Young/Old ships either, though I do prefer Hermione to have left school in the Snape/Hermione ships, simply because I'm a teensy bit uncomfortable with teacher/student relationships. Not that it would stop me a reading a fic though, if it was well written.
How and why fans take completely non-romantic relationships, run with them, and form full-fledged fanfics I think this is simply because readers see some aspect in something JKR has written that provides the seeds for imagination to grow. Some ideas work, like Harry/Snape, whilst others don't, like Filch/Harry
Is it worth theorizing and debating all non-trio ships that are overwhelmingly unlikely to happenOh yes, definitely! Simply from a literary point of view, if nothing else. Plenty of cases can be made, using canon evidence, for some of the more obscure ships such as Remus/Sirius, Snape/Lily, or Harry/Luna. Even if they are unlikely, cases can be made for why readers support these ideas - they must have seen something in the books that led them to come up with the idea in the first place. It's fun to play with ideas and argue about interpretations. It doesn't matter who's right and who's wrong - it just matters that people have fun talking about the books.
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Hermione appears to be Snape's intellectual equal. Therefore, it is only natural for fans of one or both of them to want to see them together. Hence, our love of Snape, and our desire to see him happy, drives us to place him with the only practical partner in the series: Hermione. ~LilyPotter
Using this quote as a reference (I hope you don't mind), we can see that at least one supporter of the Snape/Hermione ship feels that Snape deserves to be happy with a practical partner. Given the past actions by Snape (regardless of motive), does he deserve anything?
I think this is the basis of all good Snape/Hermione fics - fans have seen Hermione's tolerance for everyone, her defence of Snape on numerous occasions, and the fact that, intellectually, she would be a wonderful challenge for Snape. No other character fills that role and hence I think it's a very natural ship to see. It's also very beautiful, when well written. Sort of a Beauty and the Beast sort of thing (though I'm sure Hermione wouldn't appreciate being compared to a Beast

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Gratuitous Alan Rickman favouritism!!)
As for the last comment, I think it depends on your perception of Snape. I happen to think he's innocent, and very misunderstood. I felt sorry for him in his worst memory and I think there is a certain degree of vulnerability there because of that. So yes, I do believe he deserves happiness with someone who is his equal, and Hermione could be that equal...in a few years

Which is why I like the Snape/Hermione ship so much. Obviously there are going to be those who hate it, and those will probably be primarily Snape haters who just don't see in the character what those who like him do. To each his own, as long as no-one knocks someone else for their opinions. Live and let live, you know

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For this reason, homosexual and young/old relationships are considered inappropriate for advocation, as they would do disjustice to the aims of the series as a whole.
Ooh, Fish, now there's a controversial statement! Are you perhaps suggesting that homosexuality and young/old relationships are immoral? I'm not sure I understand what you mean by the aims of the series as a whole. What
are the aims? I guess we could have a whole thread about that alone!