Three is the magic number.
So, Harry's nemeses.
Harry Potter combines three elements that I've always enjoyed in fiction: fantasy, mystery, and school stories. Harry has three main opponents, one on each level.
Fantasy: His opponent is, of course, Voldemort (who always makes me think of Michael Jackson, after the way he fucked up his appearance trying to make himself immortal). I think he works pretty well -- he's straightforwardly and malevolently evil. For fantasy, that's par for the course.
Mystery: Harry's nemesis on this level is Snape, who works to foil Harry's rule-breaking schemes. This is Harry's impression, anyhow, and for the most part he's right. Snape is a fairly complex character, but the reader has to infer that from clues in the text and I don't think Harry has faced that aspect at all. He's never really thought about what makes Snape tick nor tried to research his past.
School: Draco Malfoy, not evil like Voldemort, but annoying and determined. Of the three, this is the one Harry brought upon himself, by rejecting Draco's friendship. Draco might be an interesting character, but we're really give no clue of it.
(I'm not counting the Dursleys as an enemy -- they strike me more as an obstacle that Harry must overcome.)
What frustrates me about the books is that the way both Snape and Draco are used is so superficial. If they were presented as human, if Harry had to understand something about them even as he was working against them, it would make the struggle that much richer. And they're the perfect ones to tempt Harry to the dark side, which he's not yet had to face. With Voldemort, the evil is too big and obvious. With Snape and Draco, it could be more subtle.
A flat villain cheats the hero on the literary level. As a reader, I want to be able to have at least a glimmer of empathy for the villain so that I'm invested in the conflict. Even if I hate the villain, I want to have some understanding for him. (Okay, I'm usually in love with the villain, but work with me here.)
Hence: fanon. We want to work in three dimensions. So we infer and extrapolate and talk at the pub and make shit up.
Sometimes it works, and sometimes it doesn't. But fanfiction, at least the kind I read and write, tends to explore character more than plot and we've got to have something to work with.