There are a few flashforwards to the future (I believe it’s supposed to be when Ted and the gang are in their 60s) and Ted has talked about his wife (the mother). Usually some joke about how Ted, Marshall and Lily are hanging out and Ted wonders where his wife is (because even in a future where she should be present, we still don’t see the mother).
Those flashforwards go beyond the time period of storytelling Ted, so they’re obviously married and together after they get together for good.
Skipper and Gilligan.
Funny, I always thought the Professor had his eye on Mr. Howell.
Stabler and Benson on L&O: SVU.
Yeah, he’s married, but there’s always been sexual tension between the two of them, and he’s been separated/had marriage troubles at various points in the series. Benson was pretty jealous of the hot female partner that replaced her when she was undercover, and Stabler always gets pissy when he finds out Benson is dating someone. Stabler’s wife is often jealous of Benson.
The series isn’t over yet, but I doubt it’ll ever happen.
He was carrying her up the stairs to the bedroom in the mansion they were staying in. The phone started ringing (IIRC it was Mildred) and they looked at it, then at each other, then ignored it and kept going upstairs. Fade to black.
Aragorn and Eowyn.
The George Clooney and Nicole Kidman characters in the 1997 thriller The Peacemaker sure seem like they’re going to fall for each other, but it never happens, and they remain “all business” in their respective roles as a military officer and a White House aide trying to avert a terrorist attack.
Capt. Frank Furillo and an attractive younger female detective on Hill Street Blues found themselves drawn to each other when he was on the outs with his long-term sweetie, public defender Joyce Davenport, but over a multi-episode arc they realized it just wouldn’t work out.
At the end of the movie, it seemed as if they were going to give each other a try. It wasn’t explicitly said, but I think it was strongly implied.
I was a huge fan of the show Remember WENN. It played on AMC a few years ago, was cleverly written by Rupert Holmes (of “If you like pina coladas…” fame). The series took place in a radio station during World War II. However, it was canceled after several seasons to make way for the lackluster series The Lot. Anyhoo, the lead characters Betty and Scott never got a chance to profess their love, despite a never-resolved cliff hanger where she had to choose between him or her first love Victor. Thanks a lot, AMC!
Pushing Daisies had an interesting concept, where the lead couple in love couldn’t ever hook up or the lady would die. Ned’s ability to raise Charlotte from the dead meant that he could never touch her again, or she would die again. Although, they did find creative ways to get around it, such as taking advantage of the use of plastic sheeting. (Which makes it sound dirtier than what happened!)
ETA: I almost forgot “My Fair Lady” – Professor Higgins and Eliza Dolittle never hook up, he just orders her to fetch his slippers as she lovingly stares on with a “That’s our Professor!” look on her face.
Are you sure? I’d always taken it as a given that they were shagging like bunnies during their off-hours from crime-fighting. Naturally, the modest nature of mid-60s BBC TV would not allow that to be shown, but it was hinted at - Mrs. Peel always acted like more than just a guest for high tea when visiting Steed’s flat, acting more like she lived there.
They always acted more like good friends than lovers. On the other hand, I think there were a few episodes in which Peel spent the night at Steed’s flat – not that it was explicitly stated, but that she was there for a nightcap and breakfast the next morning, that kind of thing. And it’s hard to imagine any red-blooded Englishman sharing a bachelor pad with Emma Peel and not trying something. Perhaps they were “friends with benefits.”
In any case, Peel eventually left Steed and returned to her husband, so they do qualify for this thread in that even if they did, eventually they didn’t.
Starbuck & Apollo in the new Battlestar Galactica. They had an affair for a while, but once he was divorced and her husband was dead, they still don’t get together.
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There are four movies? I’d only heard about one. I need to catch up on that before the series starts up again!
ETA: Unless that’s already happened, too. I don’t have cable. I watch TV online, or have a friend record it.
They hooked up, then she got married the next morning.
And seeing as her husband didn’t die until the last episode and she was already an angel by then, I really don’t think that side of things was particularly conducive to getting back together.
Are you sure about the kid part? The way I remember that bit of narration, he says he met her “at the airport and introduced her to my wife.” not son.
Adult Kevin actually says he met Winnie at the airport with his wife AND son. It may even have been two sons, I’m not certain, but he was definitely married with one or more kids.
Harry Stone and Christine Sullivan on Night Court.
Didn’t they get married on 30 Rock? 
I kind of tailed off the last season or two of the X Files. When did Scully and Mulder become a couple?
Unofficially, sometime after S7. Officially, the series finale and the latest film.
I don’t think it’s quite that clear cut. The final line is “Eliza? Where the devil are my slippers?” That’s not quite the same as ordering her to get them.
I’m not a 30 Rock watcher, so, huh?