So far as I know, Bob the Builder and Wendy. All the episodes I’ve seen (and what with two single-digit nieces and a nephew, I’ve seen a lot of them), Wendy clearly has feelings for Bob, but he seems to be completely oblivious.
Piggy and Kermit.
Arthur and Francine.
They got married in one of the movies.
I’ll go with Martin and Faye in Questionable Content (though the strip is still running, so I guess that could still happen).
Forgot about the Piggy/Kermit wedding.
Faye and Martin is a good one. I still am holding out hope that Faye will seduce Martin and turn Dora into an even bigger bundle of nerves and insecurities.
Ineligible as per the OP’s guidelines. While the Holmes stories were an ongoing series, Irene Adler only appeared in a single story, and was never mentioned again - no sustained tension there. And anyway, Holmes & Watson were “confirmed bachelors” (ahem, ahem) Also, IIRC, the story ends with her skipping England to marry somebody else.
What about James Bond & Miss Moneypenny? Did they ever get it on? Poor Miss Moneypenny…did so much for that cad!
Marcus & Ivanova from B5.
Janeway & Chakotay from ST: Voyager.
Holmes on Homes Mike Holmes and Pinky (Corin) A lot of tension between these two for several seasons. They always denied anything was going on.
Pinky quit the crew during the New Orleans Special. Mike never made the score.
How about Andy and Maggie in Extras? They never did hook up, did they? From what I remember, their relationship wasn’t riddled with sexual tension, but “will they or won’t they” definitely crossed my mind numerous times.
Sees to me that the “will they or won’t they” couples refer to potential relationships and if they’ll ever give it a try. Listing all these couples where they gave it a try and found out that it wasn’t meant to be and eventually fell apart misses the point. The Cheers couples definitely fall into that “They Did” camp even though they didn;t stay that way because the plot needed to move along.
Examples where there’s tension and a ongoing question about it and they end the show without ever actually doing anything at all and always wonder are much more interesting.
Watson marries Mary Morstan, whom he meets in The Sign of Four.
Ted and Robin from How I Met Your Mother may qualify - the two spend the entire first season of the show as a “will they or won’t they?” pairing. The two then get together and are a couple throughout the second season, before breaking up in the season 2 finale. The show is now in its fifth season and they haven’t shown any sign of romantic entanglement or interest since (with one minor exception).
Of course, Ted and Robin differ from the classic “will they or won’t they?” scenario in that it’s explicitly stated in the first episode of the show that they won’t end up together. The show is narrated by Ted twenty years in the future, and is structured as a story he is telling his future kids (hence “How I Met Your Mother”). And FutureTed almost always refers to Robin as “your Aunt Robin” - including within the first episode.
Practically any show resolves romantic tension if it stays on the air long enough. Usually, it’s a jump the shark event for the show. I Dream of Jeanie, Lois & Clark are examples.
I thought of one JAG Harm and Mac never hooked up.
JAG Harm and Meg Austin in season 1 same sexual tension and no hookup.
They were never really presented as a “sexual tension” pairing, though – coworkers only, no personal interest in each other.
Joey and Rachel had feelings for one another in the later years of Friends. They almost hooked up more than once but ultimately never did. Obviously not as long or important an arc as Ross/Rachel, but they did stretch it out over a couple seasons.
Oh, and I always thought there was a lot of sexual tension between Warrick and Katherine on CSI. They never really dwelt on it, but there was definitely something there. As far as I know (didn’t watch every episode) they never did get together.
Until the finale.
In the series finale, they reveal that the reason they’ve never seriously tried to be a couple is because they’d have to choose one person’s career over the other. So rather than be split up, they get married and flip a coin. Said coin never lands.
You are right in your belief that the creators waited that long because resolving their relationship sooner would have made the rest of the show anticlimatic.
Remington Steele - Remington Steele and Laura Holt
Pierce Brosnan, and Stephanie Zimbalist 1980’s series
ended in a similar way. They implied a hookup in the final seconds of the last show, but didn’t show it. It may or may not have happened.
Here’s an older than TV example: Jo and Laurie in Little Women and Good Wives. These books are often published together as a single volume, but were originally written and published a year apart. (As a kid I had a copy of Little Women alone and didn’t read Good Wives until I was a teenager, so I always think of them as two different books.) Many fans of the first book wrote to Louisa May Alcott asking for a sequel in which Jo and Laurie got married. Alcott would have preferred for Jo to remain a “literary spinster”, but decided the fans wouldn’t be satisfied with this…and also decided to make it very clear that Jo would never wind up with Laurie. Jo refuses his proposal in Good Wives, and both marry other people.
I was thinking about this last night. This must be one of the few (perhaps the only) cases of a “will they or won’t they” couple in which the audience knows from the first episode that the ultimate answer is “no”. I have to say I did find this rather annoying at the time, because I felt the writers were wasting time on a romantic plot that everyone knew was going nowhere. But I’ll give them credit for originality.
How I Met Your Mother is also an interesting case in that the title and framing device make it clear that Ted will eventually have children with a woman (I’m not sure if it’s ever specified that they actually marry). The mystery is who she’ll be.
The Wonder Years is somewhat similar in that the narration by Adult Kevin indicates that he does eventually get married and have children. Young Kevin and Winnie were on-again-off-again for several years, and if the last moments of narration were removed from the series finale it would have looked like they did wind up together for good. However, the very end of that very last episode makes it clear that although the two remain close friends for life, Kevin does marry someone else.
Katherine actually brought that up to Warrick after he rushed into getting married. She expressed her disappointment by saying something like, “The great thing about fantasies is that they might actually happen, now it won’t.”
Angel & Cordelia were treated as a potential romance from the 3rd season on, but never actually did it except in a magic-induced hallucination. I’m not sure how much that counts, though, as the other characters seemed to see them as a couple who just didn’t have sex.