That is the relationship which is maintained with so much tenderness and goodwill that it (almost) doesn't matter if it is never consummated. Mulder and Scully come to mind. Assumpta and Father Clifford before that flopped. Spike and Buffy until that flopped (and I suppose tenderness isn't the word that leaps immediately to mind, but Spike always seemed to understand her better than anyone else). Inspector Lynley and Sergeant Havers.
The characteristics of these relationships are: (1) They are working relationships; the "couple" is attached by more than just beautiful feelings. In Ballykissangel, Assumpta and Father Clifford, whether they like it or not, are the leaders of the town and act as en locus parentis over the social lives of the inhabitants. (2) The couples are characterized by an hyperawareness of each other, a kind of constant mental interference in the other person's life. Spike was bugging Buffy long before he decided he loved her. Scully would much rather hang out with "spooky Mulder" than go on boring dates. Inspector Lynley interferes to the point where Havers has to tell him to stop exercising his noblesse oblige. (3) Dialog is intimate. There's little embarrassment/self-consciousness and such. The revolving door of "does he like me/does she like me" is not just unimportant, it's long past. When, in the X-Files movie, Mulder says to Scully, "You kept me honest," he is making as passionate a declaration of intimate longing as anything that crops up in the regular to and fro-ing of The OC, Summerland or Everwood. Whether or not Scully likes Mulder is immaterial. They moved past that point a long time ago. (And the episode with the writer next door proves it—sort of.)
The writers, without giving up sexual tension, have moved the couple, and the audience, past the question "Will they get together?" to the question, "How do they get along?" I consider this to be quite a feat. Shows like Dharma & Greg, As Time Goes By and such, already, of course, operate in this area. (I don't consider that shows like Everybody Loves Raymond operate in this area because, even though the leads are married, every episode is about the husband's stupidity causing him to lose the affection of his wife which he then has to win back. Home Improvement was a bit better since Jill was more amused than upset by Tim.) In Dharma & Greg, for instance, the issue of sexual attraction and love is a given. Some of the episodes circle around the "Are they still in love?" question but the majority show Dharma & Greg working, growing and compromising as a couple until the final episode when they decide that they are strong enough to build a family together. (It is one of my favorite shows.)
So, kudos to both the consummated and unconsummated but still fulfilling and fun to watch couples of TV. And to the writers who create them.