Sabé/Obi-Wan isn't very likely in the canon SW universe, but it's the only common Sabé pairing I've seen, so I thought I'd address it here.
The Sabé/Obi-Wan pairing usually revolves around the 3 days they spent together on Tatooine. The Queen's ship is forced to land on Tatooine after it sustains heavy damage in a battle. The real Queen Amidala leaves the ship with Qui-Gon Jinn for 3 days, leaving Sabé (disguised as the Queen) and Obi-Wan behind.
Of course, the two of them don't really exchange lines in the movie, but that's because we're busy watching Amidala and Qui-Gon meet Anakin. Sabé and Obi-Wan spent 3 days stuck on a ship together; it's very unlikely that they didn't talk to oneanother.
Most fics explore those 3 days they spent together and the resulting friendship/romance that forms. The more plausible fics, IMO, explore the romance after the events of TPM. I'm not trying to offend anyone, but I just don't think that Sabé would abuse her position by having a romance with Obi-Wan while she is supposed to be disguised as the Queen.
All in all, I like the Sabé/Obi-Wan pairing. It's fun to read, and it's nice to see Sabé get some romance. :) Visit the fanfic section for some good recommendations.