At io9, Charlie Jane Anders writes about what she considers to be the 10 most romantic love stories in science fiction. These include Paul and Chani from Dune and John Crichton and Aeryn Sun from Farscape.
For my money, I found Peter David's Star Trek novel Imzadi to be the most romantic novel I've ever read. Troi and Riker are bonded in a strange way throughout the series, and this novel is an exploration of that relationship. It is put to the test, and their love ultimately transcends the space-time continuum. Very hard, very sweet.
What is your favorite love story from science fiction?
UPDATE: Matt Blum at GeekDad has a related list of the ten most tragic love stories in 'geek fiction' -- which he seems to define as to include superheroes, fantasy lit, and medieval lore. Reading it reminded me of another one of my favorite love stories: Willow and Tara from Buffy: The Vampire Slayer. It is a tale that is both sweet and tragic. It's not science fiction, but it is a related genre.