Good for them. Too bad it took them thirty freaking years.
Benedick: I protest I love thee. Beatrice: Why, then, God forgive me! Benedick: What offence, sweet Beatrice? Beatrice: You have stayed me in a happy hour. I was about to protest I loved you. Benedick: And do it with all thy heart. Beatrice: I love you with so much of my heart that none is left to protest.
Da Capo plays it straight with Junichi hooking up with Nemu, his stepsister, and all the troubles they had to face afterwards made the series' quality improve by orders of magnitude. Special mention to the extremely sad endings Miharu, Yoriko, Kotori and Sakura received. Especially Sakura. In Da Capo If, Nemu is dead and Junichi is with Kotori.
An atypical example in Da Capo II, where Koko and Yoshiyuki hook up in the very first episode (Is it possible to not get Strangled by the Red String when you do that?). They break up late into the first season, making this the "new set of complications" Downer Ending variant.
The Official Couple of Kare Kano is a fantastic instance of this trope; most of the interesting conflict starts after they become boyfriend and girlfriend in the manga version. In the anime it's the other way around, due to the amazingly bad last handful of episodes after the author threw a fit over the anime's comic elements and the director quit.
Itazura Na Kiss continues at full steam after they get married. Some fans will just tell you to skip the first season, because that's where it gets better.
Tomoya and Nagisa of CLANNAD fame (at one point a Diabolus Ex Machina steps in, with Tomoya being screwed over repeatedly, first with Nagisa's death, then Ushio's, but then they get better).
Lois and Clark of Superman. Interestingly, Seigel and Shuster wanted to give them a Relationship Upgrade early on, but DC said no. It took about sixty years and two Continuity Reboots before they found themselves back in a place where it could happen, and it took another half-dozen Continuity Reboots to break them up.
In The White Dove, when the prince has claimed the white dove/princess, the witch must let them marry. (She intends to kill them in the morning.)
In the Children Of Time series, Dr. Watson and Sally Sparrow marry an episode after first meeting each other (albeit, "Watson and Sparrow" largely focuses on their relationship, with the original events of "Blink" framing the story).
Sherlock Holmes and Beth Lestrade have a far more complicated time of it — with an entire three-part finale to work through their relationship. They do end up saying their vows, though with the knowledge that Beth will be leaving for her own time soon.
A partial list from the Deryni works: Evaine Mac Rorie and Rhys Thuryn, Alaric Morgan and Richenda Countess of Marley, Rory Haldane and Noelie Ramsay, Brecon Ramsay and Richelle Haldane, Kelson and Araxie Haldane.
The Star Wars Expanded Universe gave us more than you would think. Corran and Mirax Horn, Wedge and Iella Antilles, Tycho and Winter Celchu, Wes Jansen and his ego... Corran and Mirax are a particularly good example, though, since they got a series chronicling their Fourth Date Marriage, then several books chronicling the results of that marriage.
In the Vorkosigan Saga, Diplomatic Immunity has Miles Vorkosigan Happily Married and still at the top of his game. Of course, you could say It Runs in the Family - this is the Vorkosigans we're talking about. Miles's parents Cordelia and Aral get Happily Married at the end of Shards of Honor, continue to be awesome throughout Barrayar, then settle down to a life of (comparatively) Retired Badass-ness.
Commander Vimes of the Discworld series started out as a parody of the Film Noir detective, so obviously he couldn't be in a happy relationship. He got married to Lady Sybil in his second appearance though and it stuck throughout the wacky adventures he's been through.
Amelia Peabody's son Ramses and adopted daughter Nefret, after going through several books of misunderstanding one another, finally get married and become another Battle Couple, without repeating the style of Peabody and Emerson (although they do produce yet another generation of alarmingly precocious children).
In John C. Wright's The Golden Transcedence, after two and half books insisting that Daphne Tercius, being a version of his wife Daphne Prime, is not his wife, Phaethon reflects on the differences, tells Daphne Tercius that she is not his wife, and asks her to marry him as herself, not as a version of his wife.
In Mystic And Rider, Senneth and Tayse are both completely Badass and made of awesome, and they finally manage to get past the Anguished Declaration of Love phase at the very end of the book. In the subsequent books, in which they are together, and then married, they are far, far more awesome because they complete each other. Battle Couple extraordinaire; terrifyingly powerful fire mystic dedicated to simple human kindness marries sword-wielding Badass Normal who loves her more than life itself.
In a strange variation on a theme, in Hal Duncan's The Book of All Hours, Jack Flash/Carter and Puck/Thomas really do finally get to be together (without either one being brutally murdered by the other) ... sorta. Considering how by the end of Ink, Reality has been re-written so many times that not even Reynard/Guy/Fox could put the thing back together, and he was the damn book's keeper, the fact that they're present in any shape or form is impressive, to say the least (particularly after what happened to Seamus). In any case, they get things their way eventually, in whatever variant of reality that still includes them. If you would like directions on the various interpretations of the situation, you'll find Mind Screw on your right, and you can follow that straight down until you hit Go Mad from the Revelation (after which your confusion will no longer be a problem).
In The Eyre Affair, there are great complaints that Jane and Mr. Rochester don't get this. Thursday fixes it. Then there's her and Landen.
In L. M. Montgomery's Anne of Green Gables series, one of the bigger questions is whether Anne will stop hating Gilbert and realize she's actually madly in love with him. After getting over her stubborn pride, a rejected marriage proposal, two years dating the wrong guy, and Gilbert almost dying of typhoid fever, she finally accepts his proposal and they live Happily Married ever after, with six children.
Peter Whimsey and Harriet Vane get together at the end of Gaudy Night. As kissing is followed by marriage the last book (by Sayers) shows them happily married but with lots of issues to work out (including/triggered by the body in the basement of their honeymoon cottage).
Garion and his princess Ce'nedra spend a lot of time faffing around and bickering even during their engagement before they finally sort out their lives and admit that yes, actually, they are head over heels for each other and really if they'd been given the choice they would have chosen to marry each other anyway.
When Durnik becomes a disciple of Aldur, the Will They or Won't They? between him and Polgara is finally settled in the positive.
Adama and Roslin in Battlestar Galactica. Though she died in the finale, his actions afterwards (eg: the ring) would suggest that this still applies.
The Agathons' marriage (Karl "Helo" Agathon and Sharon "Athena" Valeri) seems to be going OK too, despite him killing her! (It was at her request and, being a cylon, she got better).
Tim and Dawn at the end of The Office (UK). Their counterparts Jim and Pam on the US version similarly get the conclusion to their ongoing Will They or Won't They? at the first episode of season 4 (though you can already tell that's where they're headed at the end of season 3).
Erin and Pete in season 9 after she dumps Andy for good.
As of the penultimate episode of the series, Dwight and Angela when they get engaged, after which their wedding takes place a year later during the Grand Finale.
Ryan and Kellyapparently in the Grand Finale when they run away together.
John and Aeryn in Farscape finally get together for good in the second half of season 4, and get married in The Peacekeeper Wars.
They were also together for much of Season 3, which went pretty well, except John had been made into two separate, equal copies, and the one she was with performed a Heroic Sacrifice. When she was reunited with the surviving John, she didn't want to look him in the eye at first.
The point where Fran and Max get married in The Nanny.
Sonny and Chad finally got together partway through season 2 of Sonny With A Chance. They've only been together a couple episodes but the show seems to have pulled it off successfully.
The X-Files' Mulder and Scully. In the 2008 movie, while they do have their issues, they appear to be happy together.
In Scrubs, there's JD and Elliot in the eighth season when they finally get together with a stable relationship after a majority of the series (aside from a break from the fourth season to end of the sixth season) went through their on-and-off-again relationship.
Turk and Carla in the second episode of the series, they eventually become Happily Married and are generally considered the most stable couple of the show.
Deliberately averted in Burn Notice. Fiona and Michael sleep together in a season 2 episode after she thought he had been killed in an explosion. In the commentary, one of the writers says that they were afraid that if the two got together, they'd play out this trope, but then realized (apparently from experience) that getting back together with an ex doesn't mean that any issues have been resolved, and often makes things more uncomfortable and complicated.
Charlie and Amita from NUMB3RS. Hooked up season three or thereabouts and have stayed a stable couple since. Charlie even asks Amita to marry him in the season five finale.
Andy and April in the third season of Parks and Recreation. So much that they get married just a few weeks after dating.
Josh and Donna in The West Wing, even though it took them seven seasons.
Ted and The Mother in How I Met Your Mother, although he hasn't actually gotten around to telling us how it happened yet.
Robin and Barney; at least they are getting married. (A scene set in 2015 had Barney "hiding" his left hand from the audience, so whether they actually go through with it, or stay married is still to be seen.) At the wedding ceremony is where Ted meets The Mother
King Arthur crowns Guinevere his Queen at the end of series four of Merlin.
In the Power Rangers Zeo episode "A Season to Remember", a look into the distant future shows Tommy and Kat happily married, with grandchildren. Fans, however, have argued with each other quite extensivly over whenever or not this episode was canon or, like another Christmas Special "Alpha's Magical Christmas", was a novelty one-shot.
In Nikita, Michael and Nikita finally get together at the end of season one, after a season of the former clinging to the misguided ideals of Division and trying to bring in the latter. Throughout season two, though their relationship is tested, they remain very much in love and are still together as of the end of the second season.
In Downton Abbey, Mary and Matthew, Anna and Bates, Sybil and Branson.
In Dept Heaven Apocrypha, flagship couple Milanor and Nessiah stumbled into a relationship quite early on. Even though they're together and that's (probably) not going to change, between one thing and another, there's still been plenty of drama to go around.
As this relationship actually happens to be a threesome with The Millstone as its third member, there's no way the drama will ever be lacking. (Although she isgetting better.)
Bryan Konietzko: Most movies and stuff, it’s all about leading up to the relationship happening. But very few things deal with 'Now we’re together,' [like with Korra and Mako]... I think those are kind of interesting things for us to deal with.
Casey Jones and April O'Neil in the second Teenage Mutant Ninja Turtles cartoon hooked up at the beginning of the third season; with the exception of an early, minor hiccup, the relationship continued strong ever since, culminating in their marriage at the end of the seventh season.