Justine Larbalestier has a great discussion going on her blog about romance. I commented there, but I kept thinking about it last night and this morning and I found I had more to say. There are lots of comments there, so go read them, and then you can come back.
OK? So: I agree with Jenny Davidson and Libba Bray, I find, in liking banter and an initial mis-alignment or problem. (Jenny calls it "painful misunderstanding," and that's just right.) But what I most want, I think, is a couple that learns from each other and grows. I also like--as several other commenters noted--some kind of equality. Thus I prefer Elizabeth and Darcy to Emma and Knightley--Knightley just doesn't (need to) change as much as Emma does, and he remains superior to her throughout, whereas Darcy and Elizabeth both need to shed their preconceptions and grow. I am also less invested in the brooding lovers--the Heathcliff and Cathy types--because they don't change or grow. Heathcliff is the same throughout--eternal, unchanging, as Cathy says of their love--and that just doesn't do it for me. Theirs seems to me an adolescent love, and I'm just not that interested in that. Or, to put it better: I don't find it romantic. I think adolescent love can be well depicted in literature--most YA literature deals with crushes and intense first love rather than mature commitment, after all, and that's entirely appropriate--but while I'm happy to read about that when it's done well (The Magic or Madness trilogy does that nicely, in fact, with Reason's attraction to Danny), I don't find it romantic.
The couple in Megan Whalen Turner's Thief books seem potentially brooding and unchanging, and one of the pleasures of that series is finding out how much they are both growing without quite demonstrating it. Which is why for me Lord Peter and Harriet are also such a romantic couple--the growth they demonstrate over several novels makes them believable, makes them a couple to root for.
I'm a little surprised that no one mentioned Gone with the Wind in the comments over there. The more I thought about the question the more I think Rhett and Scarlett fit the bill as well: she has to grow up and give up her romantic ideal of boring Ashley Wilkes, and he has to rein in his cynicism and admit there's something that motivates him beyond self-interest. They are right for each other without knowing it, and they keep getting it wrong. The fact that they can't ever be in love with each other at the same time is what makes the novel tragic rather than comic, of course, and I tend to prefer the comic (and, yes, there's all sorts of baggage with Gone with the Wind that I'm not talking about right now). But it is romantic, absolutely.