For all Doctors in general, The TARDIS itself — see "The Doctor's Wife".
For the Ninth Doctor: Rose Tyler.
For the Tenth Doctor (and his half-human clone): Rose Tyler.
Mickey Smith and Martha Jones.
For the Eleventh Doctor: River Song, and later Clara Oswald. Note that the latter relationship is downgraded to platonic friendship upon his regeneration into the Twelfth Doctor (at first; see below). The Clara relationship is actually made official when the Twelfth Doctor states in dialogue in "Deep Breath" that his previous self considered himself to be her boyfriend.
Amy Pond and Rory Williams.
Jenny Flint and Madame Vastra.
Clara Oswald and Danny Pink, after her relationship with the Doctor is downgraded to simple friendship. Alas, Danny is dead at the end of Series 8.
For the Twelfth Doctor: Clara Oswald, with whom his relationship is back to more romantic footing after Danny's passing. Later River Song.
In Torchwood, Gwen and Rhys, and Jack and Ianto are the Beta Couple. Then Ianto is killed by the 456.
Forty-five years after their original run, The Sarah Jane Adventures story "Death of the Doctor" made official couples of two sets of classic series companions: Ian and Barbara, and Ben and Polly!
Power Rangers has a few, mostly involving the Red Ranger, most notably Kimberly/Tommy a.k.a. "Tomberly" from MMPR, who shared several (and indeed the first) of the few on-screen kisses that went down in PR history.
Kat and Tommy were indicated to be married in the distant future once and there's really nothing that's said otherwise since then.
The biggest official couple in later series is Wes and Jen, where part of the plot is that Jen's fiance Alex (who looked exactly like Wes) was killed by the Big Bad and she was slowly warming up to Wes and the possibility of a Second Love.
Tyler and Shelby get together after a season and a half of dancing around each other.
Calvin and Hayley have been together for a least a year prior to the start of their season.
Kamen Rider Ryuki has Ren and his fiancee Eri as an established couple; and also Kitaoka and Reiko as a Will They or Won't They? of this trope. In the movie, Shinji meets Miho and they are an implied official couple themselves.
Shinnosuke Tomari and Kiriko Shijima from Kamen Rider Drive. They are one of the very few unambiguous main couple in the entire franchise. The "Where Are They Now?" Epilogue in the final episode even mention that they got married and later got a kid. Said kid even appear in the Surpise Future movie when he travelled from the future. The crossover movie with Kamen Rider Ghost also ends with their wedding. Even further, the sequel novel set two years after the end of the series shows Kiriko taking a maternity leave to take care of their newborn child.
Despite the writers' attempts to the contrary — "PK Tech Girl", "I Do, I Think", and even "Eat Me", for example — there was no doubt who the official couple on Farscape were. John and Aeryn were awkwardly falling into tight spaces together or each other's arms in the first episode.
NUMB3RS has two: Charlie and Amita for one, who have had tension since they were introduced, and Larry and Megan, which nobody saw coming.
Ross and Rachel in Friends, whose convoluted romantic relationship becomes a major plot point in the series. Monica and Chandler shared this with them in later on, as they were together for over half the series and served as the romantic and emotional rock of the show. This contrasted to the high profile but irregular Ross and Rachel, meaning they also doubled as the Beta Couple although they led many siginificant storylines.
Sam and Diane in Cheers, though Diane left in the Season 5 finale. The original intention behind the characters, in fact, had involved a Katherine Hepburn/Spencer Tracy dynamic. After this, there was some teasing about Sam and Rebecca coming together, but it didn't really happen.
Star Trek: Enterprise had some confusion over this as there was some hints towards a T'pol/Archer romance, but was actually opposed by the actors themselves as it was a senior officer/subordinate relationship and generally inappropriate. Although there was plenty of T'pol/Trip as well, set up from the pilot with their intimate disinfecting and having Slap-Slap-Kiss vibes for the first two seasons. It became more overt in the third season and while it never became official in the series it was stated they did spend some time actually together.
Star Trek: Voyager: Neelix and Kes, then Tom Paris and B'Elanna Torres, but never Janeway and Chakotay to fan disappointment. In fact, given that the need for everyone to start pairing up was lampshaded early in the series (as they thought they'd take 70+ years to get home) it's surprising how little romance there was on the ship.
Star Trek: Deep Space Nine was more character-driven than the other shows, being set on a space station so it explored romances more.
Captain Sisko and Cassady Yates. In fact this was made possible because she was a freighter captain who frequented the station, meaning there was no chain of command to worry about. All other Trek captains had problems with never being able to stay around long.
The West Wing has Josh/Donna after seven seasons of Will They or Won't They?. There's also CJ and Danny, who are on-again, off-again throughout the series, but confirmed married and with a child in a flashforward at the beginning of the seventh season, President Bartlet and his wife Abbey, who are mostly Happily Married, and President Matt Santos and his wife Helen. Fan-Preferred Couple Zoey and Charlie were last seen together in season six, but their eventual fate is left ambiguous.
The American soap As the World Turns has quite a few "super couples", with a clear indication that they are meant to be together. One such super couple is Luke and Noah. Unlike their heterosexual counterparts, they have actually no other possible characters to hook up with, their story lines consisting instead of breaking up and making up every few months. In a soap, you can tell a couple is "truly official" after they make up for the third time. However, with the introduction of Dr. Reid Oliver, Luke has a viable second love interest, and is currently wanting Reid to fight for him. Reid did, and Luke and Reid became the official couple with Noah barely seen.
Susan and Mike on Desperate Housewives were set up this way from day one; in fact when they finally got married in the third season finale, there was a Lampshade Hanging from Susan's daughter Julie: upon the usual "reasons they shouldn't wed" question she replies "Are you kidding? They've been dragging this out for three years." Even after they broke up in a five year Time Skip, fans are just waiting for them to reunite. They Do.
Stargate SG-1: While they can't be together until one of them quits the military, Jack and Sam are very much the "it" couple of the show. According to Word of God, they were originally not intended to be this; but when the powers that be realized the fandom had latched onto the brilliant onscreen chemistry between Richard Dean Anderson and Amanda Tapping, they decided to go with it.
Depending on how you view deleted scenes, this scene from the "Stargate Atlantis" episode "Trio", basically makes Sam/Jack canon. The DVD intro to the scene has the Powers That Be very explicitly state that Sam is referring to Jack and they are a couple. At least one writer has said that as far as he's concerned, Jack and Sam got together after "Threads" and have been together ever since.
Daniel/Vala was this in the last couple seasons.
Much to the dislike of several fans, and the great pleasure of several others, Rodney and Keller on Stargate Atlantis.
Sheppard/Weir was an example where the actors played their characters together like this, even if the writing didn't exactly follow it. Howeever like Jack and Sam, any relationship between them would be disapproved of by their superiors because of their shared command of Atlantis, the writers could have been setting up a similar unofficial romance without writing anything overt.
Battlestar Galactica (2003) had President Laura Roslin and Admiral William Adama, who, in contrast to the other couples on the show, took four years to finally acknowledge their feelings openly (they got off to a bit of a rocky start, what with the whole 'interferring in the military/coup d'etat' thing), although they first kissed in Season 2 when Roslin promoted Adama to Admiral.
Besides them, Morgan and Anna in the first two seasons as well. Afterwards, Morgan and Alex.
Ned and Chuck in Pushing Daisies, much to the annoyance of Ned/Olive shippers.
Viktor and Sierra in Dollhouse fell in Love at First Sight, and keep doing it with every new personality they're given, and when they don't have personalities.
Richard Castle and Detective Kate Beckett from Castle.
Robin Hood and Lady Marian in Robin Hood. So obvious that it hardly warrants mentioning, except that the Fan-Preferred Couple of Guy/Marian had some fans vilifying Robin, listing the reasons why Guy was a better match for Marian, and clinging to the hope that they would somehow end up together. Ultimately Guy murdered Marian, effectively ending both ships, and yet there were still some that complained that it was Robin and not Guy who got the Together in Death scene with Marian at the end of the show.
Lily and Marshall have already been together 9 years when the series begins, and flashforwards show them still being Happily Married in the year 2029. However, once they got married they mostly became the Beta Couple.
The series finale reveals that Ted and Robin are the official couple, despite The Narrator having denied it since the beginning.
Gilmore Girls had several Official Couples: Lorelai/Luke and Lorelai/Christopher and then Rory/Dean, Rory/Jess and Rory/Logan. By the time the show ended though, Lorelai and Luke were endgame but Rory was single. Naturally, this lead to Shipto Ship Combat. There were also the Beta Couples in Sookie/Jackson, Lane/Zach, and Paris/Doyle.
The X-Files: Mulder & Scully. As to when they got together, the series is never clear and it is a constant debate among fans. However, most seem to place it somewhere during Season 7. Funnily enough, Chris Carter insisted that Mulder and Scully were never supposed to be anything but platonic work partners. The writing, however, suggests otherwise.
Glee: Rachel and Finn are the flagship couple of the series. Everything romantic that revolves around these two characters, even if it's involving other characters, generally ends up related in some way to them as a couple.
Because of this, Kurt and Blaine seem to have be promoted from Beta Couple to the Official Couple. They got together in the middle of season two and as of the season five premiere are engaged.
There is also Emma and Will. Happily Married as of the Season 4 finale "All or Nothing."
Hannibal: At the conclusion of season 3, not only are Margot and Alana happily married with a son, but Hannibal and Will confess their mutual feelings after killing together for the first time, embracing lovingly while nuzzling. In the end, they either die in each other's arms or fake their own deaths so they can run away together.
It has been made official that they did not die and talks about a fourth season began mid-2017. Hannibal and Will will be together in the fourth season, should it come to pass.
Psych sets up Shawn/Juliet over and over and over again...and then, at the end of season three, has Juliet confess that she is, in fact, in love with Shawn, while he was on a date with another girl. Since then, it seems to come up occasionally, but it's hard to tell if they've both moved past it or are just waiting for the right moment again. In Season 5, they're officially together.
Brenda and Dylan were the main official couple of Beverly Hills, 90210 in the early seasons, but the pairing of Dylan and Kelly became so popular at the time that he ended up with her instead. Of course now, most fans wished he ended up with Brenda instead just as they wished Kelly ended up with Brandon. Also, David and Donna ultimately end up with each other in the end.
Niles and Daphne in Frasier managed to be an official couple throughout eight whole years of Unrequited Love, UST, and Will They or Won't They? before even making a move, never mind getting together, and despite Niles being married to someone else for the better part of that period. They were relegated to Beta Couple afterwards.
Eric and Donna in That70s Show. Fez and Jackie suddenly become this in the final season, much to the disgust of both Hyde/Jackie and Kelso/Jackie shippers.
Days of Our Lives has a few. No matter what happens or how bad it looks, there's no way Bo and Hope, John and Marlena, and Jack and Jennifer don't end up together. There's also, of course, patriarch and matriarch Tom and Alice Horton.
While Passions had several official couples, the most prominent ones were Ethan & Theresa and Luis & Sheridan, although only the former ended up together with Luis ending up with Sheridan's niece Fancy, and Sheridan ending up with Luis' brother, Antonio, her first husband.
John Sheridan and Ambassador Delenn of Babylon 5, who, as mentioned elsewhere, walked through fire for their love and lasted the entire run of the show. (Sheridan doesn't appear until season two, although a later-but-earlier TV movie indicates they met prior to the series.)
ER: While almost everyone in the main cast had temporary romantic relationships with each other, the following couples got a lot of focus and became endgame for good:
Doug and Carol.
Mark and Elizabeth, until Mark's death. She reveals to Benton in the series finale that she hasn't been serious with anyone else since Mark.
Benton and Cleo.
Kerry and Sandy, until Sandy's death. Kerry reveals in "Breach of Trust" that she hasn't been able to move on since Sandy's death, and that moving to Florida with their son Henry will help her move on.
John Crichton and Aeryn Sun of Farscape. The chemistry between them left many a fangirl panting. And there was a lot of chemistry, right up until the very end. (Also a very neat avoidance of Shipping Bed Death.)
Snow White and Prince Charming. They start out the show getting married, so even though in the present they aren't together, ya know it's gonna happen again eventually. Also with their actors in real life, too.
As of season three's finale, Killian/Captain Hook and Emma.
In The Closer, Brenda Leigh Johnson and Fritz Howard start out as friends with UST, reunited when Brenda's new job moves her close to him, and their relationship progresses to dating, engagement, and marriage in a fairly predictable manner.
Dwight and Angela were this in at least the early seasons, and even though they haven't actually been together in over five years, their relationship has remained a big part of the show throughout it's run. No matter how bad things seem at times, something always happens to make them revisit their feelings for each other. Add to that a nice dose of Will They or Won't They?, Unresolved Sexual Tension, and Unrequited Love Switcheroo.
Michael and Holly from the end of season 4 onwards.
Later, Barbara and Tom; they get married in the final episode of series 6.
The 100 is not overly concerned with romance; most potential romances either never get off the ground or crash and burn shortly after they're introduced. The notable exception is Lincoln and Octavia, who hook up halfway through Season 1, and, while occasionally seperated by circumstances, always find their way back together and never waver in their devotion to each other.
Elizabeth and Henry McCord on Madam Secretary. Unusually for this trope, at the start of the series they were already Happily Married with three children — and miraculously, have stayed so despite the rather ridiculous amount of stress their marriage is put under over the course of the show. They've been cited as the healthiest example of marriage on television.
Pretty Little Liars: All four girls date several different people throughout the series, but end up with their longest-standing and most prolific love interests at the end of the series:
Aria and Ezra.
Hanna and Caleb.
Emily and Alison.
Spencer and Toby.
''Grimm: Nick and Juliette. Subverted later on, when Juliette becomes a Hexenbiest, and her personality changes as a result. On the other hand, Adalind becomes gentler and much friendlier as a side effect of the Hexenbiest-blocking potion. Eventually, Nick and Adalind become this trope, and Juliette (now calling herself Eve) remains by herself for the rest of the show. Nick and Adalind even have a child together, despite the baby being a result of a Bed Trick by Adalind (she made herself look like Juliette).
Scrubs has Turk and Carla, Dr. Cox and Jordan, and J.D. and Elliot.
Schitt's Creek has Ted and Alexis, David and Patrick, Roland and Jocelyn and the matriarch and patriarch Johnny and Moira Rose.