Jenny: Even if she lived, doomed in the end. I think this story has it about right. Eventually Buffy will get in the way. Imagine that comment carrying through for the rest of these characters.
Ethan: Okay, I can see this, if only because Giles comes to us with a pre-existing relationship with everybody's favorite chaos mage. But I can't see it lasting. Ethan threatens Buffy, and Giles cannot tolerate that. I'm willing to be convinced on this one, though.
Willow: So tempting, because Willow is the Scooby easiest for me to identify with. But a) not Buffy, and b) not enough self-esteem. My take on Giles is that he needs somebody strong to pull him out of his shell. Willow seems the likeliest of the Scoobies to form a strong friendship with Giles. At least pre-Tara Willow. The later Willow, not so much. (The later Willow is less interesting to me than the earlier Willow. Possibilities and potentials are always so much more enticing than their collapse into a single result. But maybe this is because the high school library Scoobies are the ones I love best.)
Xander: Just can't see why Xander would interest Giles. I've read some fun G/X fic, but it requires too much suspension of disbelief for me. How can these two have a conversation?
I often ask that question about Buffy as well. What would Giles talk about with her? Would he find that relationship intellectually satisfying? She's so often such an airhead. The Magickal Bond Thang trumps this objection, though. The Watcher will always have a lot to talk about with the Slayer. The airhead thing could of course just be a Buffy pose, a defense mechanism.
Oz, Cordelia: Kids. Oz is at least an interesting and deep character. Can't see Giles getting past the 25+ year gap to be interested in either of these.
Anya: The series gives them the relationship they're best suited for.
Joyce: I've seen a convincing case made. She's at least an adult. I see the tension between their roles-- the Watcher and the mother of the Slayer-- to be a major obstacle for these two. Joyce is likely always to blame Giles for sending her daughter out every night into danger. (See the season 3 opener.)
Wesley: I haven't watched Angel, so I don't know if the Angel edition of Wesley is more interesting than the character we saw in season 3 Buffy. The S3 Wesley is too much of a threat to Giles, I think. The guy is there to take his Slayer away, after all. And there's the whole blueberry scone problem.
Giles in England, season 6, is another matter. He's made his emotional break with Buffy. One expects him to be actively working on assembling a life for himself. Lots of scope here for the interesting OC, such as in the excellent and lamentably unfinished Watcher series by vatwoman.
I should add that I've read and enjoyed good examples of all of these pairings. I can't convince myself to write them, though.