Ummmm, I thought about this one for a few days (seriously) and I truly could not think of a single pair of characters that I wanted to "get together" that weren't ever in some sort of doomed romance. To be completely honest, I think most of them work much better as simply friends, since their idiosyncracies and shortcomings tend to be what they hope are resolved by said romantic entanglements. Anya was looking for identity with her relationship to Xander; Xander wanted a woman who made him feel like a man. Neither was self-sustaining outside of themselves, so to fully make it work between them, they'd have to fully address their weaknesses separately, which they did by Season Seven. I'm glad Joss didn't put them back together, though, even if it did mean that Anya was gonna be sliced at the end of the season. Buffy spent so much of her time maintaining a hero's complex that any relationship she had made her weaker and more dependent than she already was. Angel's banishment to a hell dimension was a major turning point for Buffy, since after that, she started to cut herself off from her friends and family, ultimately pushing away Riley and then delving into a deeply emotionally and physically abusive sexual relationship with Spike. Oz and Willow were I think a great couple, in that neither had any type of power struggle during much of their relationship, and then Tara and Willow initially had a similar dynamic, until Willow became a selfish asshole and decided mind-rape was better than dealing with problems. After Tara's death and Willow's subsequent vengeful lesbian act, any relationship was going to be plagued by her past.
Actually, looking back on the initial question, I'd like to rephrase it to "two characters I wished hadn't gotten together," because hello, Willow and Kennedy. This is not because I disliked Kennedy, which I did; the character was insufferable and even called herself "kind of a brat," but I don't think Willow was ready for another relationship. I'm a firm believer in that, if you haven't dealt with your issues (that played a major role in the demise of your last relationship and, oh, turning evil), you probably shouldn't jump into another pairing. And Willow's issues were huge. She murdered Warren, threatened to turn Dawn back into energy, nearly killed Giles, and then tried to destroy the world. A few months spent with a Wiccan coven in England ain't gonna rub that blood out, guys.
I suppose the only character that I wish would have gotten into some type of relationship would have been Giles. His romance with Jenny Calendar was such a tragedy, in so many ways, because I think they brought out the best in each other, despite the fact it only spanned a short time. With Olivia, his world was just too scary for her, which, to be fair, I get. After that, Giles spent much of his time trying to figure out where he stood in Buffy's life, without doing much with his own. It's not that I think he didn't get a sense of purpose without having someone to bone, but I really dislike the notion that, as you get older, romance no longer has a place in your life because it's what frivolous young people do.
Granted, even if he had been given an opportunity to have a girlfriend, it would have probably ended badly, because who am I kidding, this is Joss Whedon we're talking about.