I don't gravitate toward romantic stories, although I do love passion and sex in my fiction. I sometimes find romantic pairings, especially if a good deal of the plot is tied up in the eventual getting together of the couple, to be tiresome. As I made this list, I realized that many of the couples I picked aren't necessarily romantic; most are certainly not role models for healthy relationships. Still-- I love 'em! (NB: I stopped at about eight because I was starting to get truly silly with my definition of 'couple'; I may tackle this one again in the future because it was far more challenging than I anticipated!)
Nick & Nora Charles from The Thin Man. While I do love -- I mean love -- the Nick & Nora movies starring William Powell and Myrna Loy, the Mr and Mrs Charles of Hammett's original novella are a far cry from the jaunty, good humored couple seen on the silver screen. Their motives for marrying are questionable and they're both horrifically amoral. Worse, they're captivating.
Josephine & Napoleon from The Last Great Dance on Earth. Another trilogy with an amazing heroine in a complicated, difficult marriage. Author Gulland created a vibrant woman in Josephine; by the end of the trilogy, I was in love with her! Historically we know Napoleon loved Josephine; Gulland's writing makes it clear why these two had -- for a time -- such an amazing relationship.
Mannie & Mike from The Moon Is a Harsh Mistress. Okay, so I'm definitely pushing the definition of 'couple' with this one, but I can't resist. The Moon Is a Harsh Mistress is a guilty pleasure read, and pretty outside the norm of my typical reading tastes. Technically, the couple of note would probably be Mannie and Wyoh, but despite their desire for each other, I didn't find their relationship as compelling as the one Mannie had with the sentient computer Mike.