You know what just occurred to me? Harry and Hermione are the incomplete halves of one whole. They complement and compensate for one another in every way possible! Which makes them beyond perfect for one another and also explains why there's so much more real chemistry between them than the "anvils" of R/Hr.
Don't worry, I'll explain...
Look at it like this: Hermione is good at just about everything, right? I mean, everything that involved brainwork and school. But the one thing she's not as good in (she's still good, though!) is Defence Against the Dark Arts. And, coincidentally, DADA is what Harry is best at, and he's not so good at the other stuff. Meaning, of course, that Harry needs Hermione for everything else (JKR has said this herself) and Hermione needs Harry for DADA (she says so herself in OotP).
Then we've got their other talents. Harry excels at Quidditch, while Hermione is miserable at it. Here we have them compensating for each other's weaknesses. Harry = physically capable; Hermione = dependent on Harry physically. Similarly, as far as research and spell-mastering goes, Harry needs Hermione. Hermione = book goddess; Harry = dependent on Hermione to save his butt with special spells (think of GoF!)
However, Herons have argued that Harry and Hermione share no interests. This is quite wrong, because in spite of compensating for each other's weaknesses, they also have a solid foundation of shared interests and humour. They often make each other laugh (this is most evident in OOtP and HBP) and it's not the way Ron makes them laugh (his way his more obvious). They often pick up on things no one else notices (Malfoy's "dogging"). And, in addition, they do have a lot of shared interests that would bolster their companionship and make sure that it isn't just dependence that keeps them together.
Hermione's SPEW, for example. While Harry doesn't take to it much, it has to be noticed that he is the only one (apart from her) who really cares about the house-elves. Noticeably, throughout Ootp and HBP, he begins to sympathise more and more with SPEW (his response to Hokey's arrest in HBP). Harry has also proven that he can talk to Hermione about deeper stuff, like relationships. They understand one another. The only "understanding" barrier is Quidditch, but even then, Hermione has never shown anything but support of Harry while on the pitch!
Both Hermione and Harry have also been told they would make good Aurors, and while Hermione's never shown an active interest in it, it's interesting that they share those qualities and that this would imply that she would understand a great deal of it if Harry had such a job (think of their domestic life... "how many Dark wizards did you round up today, dear?" "Oh, the usual" "I know, I understand... oh, Harry, you're hurt! I got some Murtlap tentactles together and you can ease the pain while you tell me about your day!").
It just seems to me, more than more with each re-read of the books, that Harry and Hermione complement each other, compensate for each other's weaknesses, need and respect each other, and seem to almost be two bodies sharing bits of the same soul. No other character in the series shares this with either or them. How can anyone deny it?
As for romance, well, I believe it's going to happen, and the above is just one of the many reasons why. Harry and Hermione's growing, gradually-more-romantic bond is subtle, but that's really what makes it so special and so much more real, isn't it?
