For Dragon Age Origins, it would have to be Morrigan and/or Alistair. Sort of breaking through Morrigan's walls to a point and having her come to realize her feelings is really nice, and I think Alistair works really well depending on your background in that game. For me, I boned Zevran then ditched him, tried to romance Leliana but failed, so I was left for Morrigan. Despite not really being my first choice, I was pleasantly surprised. Witch Hunt could have been better, but I felt it was tailored made to be for those who romanced her.
As for DA2, anyone not named Anders. Seriously, after what he does in that game? Screw him. Merrill isn't any better, since her whole arc involves not listening to you at all if you try to be good. Even when you try and tell her not to do the demon stuff, it only leads her into a rivalry (almost automatically at one point I believe). Besides, I always saw her as a horribly done Tali (from Mass Effect), which didn't help matters. Isabella is what the game pushes you towards I guess, but she never really...pays for her actions? She's responsible for so much, and she isn't really a super bad person, but she left me and never came back, so the hell with her (a case of Friendship just being RIGHT under the requirement). Even if she comes back and you want her to pay for what's she's done, she apparently sees this as a betrayal. No, its called consequences Isabella.
Don't really know how Nathaniel's romance works out, although I know it doesn't lead to anything physical, just romantic.
I romanced Fenris, which I couldn't finish because my friendship with him was just shy of reaching that point (and getting him to such a high level as a pro mage Hawke felt like hard work too). But I always liked the fact of him falling for Mage Hawke, and sort of learning from the experience to be a better person. Course...that doesn't really happen sadly (To him you are one of the few exceptions, and that's it), but the potential always felt nice.
Actually, I think all the DA2 romances had great potential to affect future casual conversations with them in the story, even if you aren't in one of those "romantic conversations" that you get into. Could really see the story evolving and going in different directions/changing certain outcomes. But like many things DA2 related, it wasn't meant to be. Given the option, I honestly probably would have gone for Aveline or Varric since they were the best characters in that game.
tl;dr: Morrigan and Alistair for Dragon Age Origin's. Nobody too particular in Dragon Age 2, but I was partial to Fenris.