If this were for a broader audience, I would need to start off with some backing-up of the statement "Snape is an interesting character." For the moment, I'm going to take it as read that Snape fascinates many in fandom.
One thing I find fascinating is that Snape is endlessly faceted. I joked once that I had a hundred Snapes in my head, and I'd written about a dozen of them at various points. I think it's absolutely true; and different pairings allow us to imagine him as completely different kinds of people.
( Part I: Why Snape? Or, Why can we speculate about Snape? )
Part II: Why fanfic?
Answer: Fanfic allows us to speculate in a deeply immersive, satisfying way: narrative. I mean, why not just write an essay describing what Snape would be like if his father had killed his mother when Snape was only four, and he'd gone to live with some distant relatives, the Blacks and their three daughters, Bellatrix, Andromeda, and Narcissa? Because it's a hell of a lot more fun as a story. Humans love stories. It's in our nature. They make us feel, and we love to feel. (It's the reason why "One death is a tragedy. A million is a statistic." -Joseph Stalin. But I'm digressing again.)
Now we have two things: an interesting character with a lot of blanks we can fill in (Snape), and a compelling method of doing so (story-telling via fanfic). This is why I love to write about him. He's so versatile.
( Part IIa: Why *romantic* fanfic? )
( Part III: How Specific Characters Work With Snape )
Now for the audience participation part of the essay! How do specific characters bring out specific sides of Snape? I will add to this section if anyone has any comments or suggestions. Let's see what you think!
( List of Various Characters )
(cross-posted at IJ; please comment there!)