7th Heaven: Matt and Sarah go through a few rough patches, but remain together and in love.
30 Rock: Tracy and Angie Jordan, although Tracy has to maintain an Urban Legend Love Life in order to keep his Celebrity Endorsements. It's kind of weird, but, to give an idea, he says that Angela threatens to divorce him if he doesn't have an affair: the image of promiscuity and general "coolness" is what keeps the family afloat, moneywise. As it turns out, he can't bring himself to have an affair; he's just too devoted.
Sheridan and Delenn, in season 5. They have their disagreements, but nothing ever really threatens their relationship. This despite knowing that Sheridan only has twenty years to live; they seem to have agreed to live in the moment and enjoy every minute they have together.
Jeffrey Sinclair and Catherine Sakai: their story is told in the canon novel To Dream in the City of Sorrows, and Word of God states that he does find her in the past.
Battlestar Galactica (Reimagined): Though they go through just as much hell as everyone else, Helo and Athena are happily married with their kid, their love for each other (and for Hera) never wavering. You really get a sense of their trust in each other after Helo fraks Boomer, thinking she's Athena, and Athena doesn't even think about accusing him of anything.
Chuck: Ellie and Devon "Captain Awesome" Woodcombe don't get married until the end of Season two, but they provide the main stable relationship in the show.
The Closer: Despite Married to the Job tendencies, Jurisdiction Friction and alcoholism, Brenda Johnson and Fritz Howard are still passionately in love with each other. They've had their drama, but there's no doubt that they're it for each other.
CSI NY: Got in on it with Danny and Lindsay. They had a tumultuous courtship,pushing each other away repeatedly and Danny slept with someone else (Rikki Sandoval), and there was stress during Danny's stint as a sergeant in early season 8 but things seem great now, especially with Lucy having come along.
Tom and Lynette Scavo. They do have their turmoil and they're broken up for nearly the entire final season until reconciling permanently in the finale, but they never stop loving each other.
Mike and Susan are generally happy together during the times when they're in a relationship (and when they're not it's because of some external obstacle, not friction in the relationship.)
Dharma and Greg: Dharma and Greg Montgomery. Most of the comedic tension of the show came from the antics of their friends and parents (who were also happily married). Though, the season nine premire of Two and a Half Men shows them as a bickering, on-the-verge-of-divorce couple.
Lloyd and Barb Diffy of Phil of the Future: They are united when it comes to teaching their children and still go on dates. One such outing was to the original production of Romeo and Juliet in Shakespeare's time. They got dressed up and everything.
Jerry and Theresa Russo of Wizards of Waverly Place demonstrate realistically how a happy marriage isn't a perfect one. They run a business together while raising three children. This causes tension to rise on a daily basis but they work through it. Case in point: Jerry gave up his wizard powers so he could marrry Theresa and hasn't regretted it since.
George and Nora of Life With Derek: The premise of the show is their marriage joining two families together. This causes turbulence and a number of episode plots but at the end of the day they're glad they're together.
In finale of series 6, the Doctor is now happily married to River Song. She may spend her days in prison, but the nights... that's between them, eh? Sadly for her, though, they keep meeting up in the wrong order, and younger versions of him have no clue what's going on.
Amy and Rory are a somewhat surprising example in that they appeared to be a repeat of the Rose/Mickey situation, where the woman was more into the Doctor than she was her nominal boyfriend. The events of "Amy's Choice" made Amy realize how much Rory meant to her, and after a temporary parting via the Crack they eagerly married. The two do split between series 6 and 7, but reunite after they sort out some miscommunication and are still together when they're sent back in time.
Dollhouse: This seemed to be the case with the senator and his wife. When he's drugged and possibly raped, his first reaction to the blackmail attempt is to take the call girl to his wife. For once, a person who didn't cheat but is in circumstances that can lead to Mistaken for Cheating does the sensible thing and plans to explain the situation to their SO instead of trying to cover up the non-affair for fear of not being believed. And then, the wife turned out to be evil and possibly not even legally his wife.
Robert and Cora Crawley, the Earl and Countess of Grantam, have been Happily Married for twenty-three years. They've actually been married for twenty-four years; it took a while for Impoverished Patrician Robert to fall in love with American heiress Cora after he married her for her money. They suffer several rough patches in Season 2 Robert feels neglected by Cora during the war and considers an affair with one of the maids though he can't bring himself to do it, in Season 3 Cora blames Robert for Sybil's death, but they get back on track and clearly still adore each other. Just look at their faces when Robert surprises her in the Season 4 finale.
Star-Crossed Lovers Tom and Sybil had it rough but after they finally get married are apparently blissfully happy.
Eight Is Enough: Tom and Joan Bradford. That is, until Joan was killed off because her actress died. Tom marries schoolteacher Abbey Abott in season 2, and this was also a happy marriage.
Family Matters: Carl and Harriet Winslow. Also Estelle "Mother" Wisnlow and Fletcher later on.
Firefly: Wash and Zoe. Their marriage is stable and happy, and their sexual chemistry is amazing. They might fight and argue, but they obviously love each other very deeply and they back up one another frequently. Zoe dreams of having a baby together, despite the fact that things are tough in their Crapsack World.
Frasier: Niles and Daphne. After they work through their Unrequited Love Switcheroo thing anyway. They're happy and relatively frictionless for exactly one season (10), then Daphne gets pregnant and becomes an overbearing, hormonal harridan (she seems to be back to normal in the final episode, once her child is born).
Freaks and Geeks: Harold and Jean Weir. (Series creator Paul Feig said that he intentionally chose for the Weirs to have a happy marriage partly because his own parents had one, but mostly because he was sick of all the dysfunctional parent couplings so prominent on television.)
Friends: Monica and Chandler in the last three seasons. The universe puts them through a lot early on: A long-distance relationship, unemployment, infertility) but they remain incredibly happy and adore each other. They're especially impressive given their significant emotional baggage that stacks the odds against them. Namely's Chandler's parent's terrible marriage and home life which caused his Commitment Issues, Monica's insecurity from Abusive Parents and their highly neurotic natures.
Ghost Whisperer: An interesting example is Melinda and Jim, because they are the main couple, the relationships of her friends get barely any attention, they hardly ever fight, they don't have kids, and it's a drama. But then, this show is sap central. This is challenged when Jim dies. He Body Surfs into a dead guy named Sam and gets amnesia. Naturally, he (Jim; Sam "crossed over" immediately after dying) gets better.
Owen and Christina, two very damaged people, seem to take that road, thanks to some Character Development of the later in season 7.
Callie and Arizona. Though they don't appear to be legally married, as Washington State doesn't currently recognize same sex marriages. But they share a good relationship.
Happy Endings: Brad and Jane-despite the fact that they often have (humorous) arguments, their fights never last more than an episode. They're also crazy into each other to the point of being Chivalrous Pervert.
The Honeymooners: Ralph and Alice are always fighting, but the idea that they might ever break up is as inconceivable as Ralph actually knocking Alice "right to the Moon."
How I Met Your Mother: Lily and Marshall, despite breaking up at one point, are happily married and completely love it that way.
Harry and Jennifer Crane are noted as Happily Married from the beginning but then Harry has a one-night stand with Hildy (a secretary) after a typical drunken Sterling Cooper party, and has hell to pay for it when Jennifer finds out. Fortunately for him, she forgives him; he doesn't seem to so much as look at another woman after that (until season 4, when he has apparently morphed off-screen into a bit of a douche).
Pete and Trudy Campbell get to Happily Married ahead of everyone else on the series (besides Harry and Jenny) after working through (in agonizing detail) Pete's problems with infidelity and adoption. The Campbells dance a most enthusiastic Charleston at Roger Sterling's wedding, and in the end Pete, after his last indiscretion, decides he never wants to be away from Trudy again. After that, he's seen consulting her about serious stuff fairly often (like the decision to hop over to the new Sterling Cooper Draper Pryce). And then in Season 5, he cheats again...but comes to have mixed feelings about it. The move to suburbia seems to have something to do with it.
Averted with other. Roger and Mona Sterling? Divorced. Roger and Jane Sterling? Shot to Hell, ending in divorce. Joan and Greg Harris? Complicated at best, ending in divorce. Sal and Kitty Romano? A lie. Don and Betty Draper? Divorced.
Ken Cosgrove is about to get married, just as he's joining SCDP (and thus rejoining the show). Let's watch as the writers make his life totally miserable! Though it appears, when the higher-ups at SCDP try to get him to use his wife to land an account and he shoots it down, that their relationship may actually be based on (gasp!) love and respect!
Peculiarly, Don and Megan Draper, despite ups and downs, seems to work, not being seriously threatened until literally the last minute of Season 5, at which point it cuts to black, Sopranos-style.
Hal and Lois. The show is unusually frank about the importance of their sex life to their conjugal stability: they have sex twice a day, on average, and when some unusual circumstance makes that average slip, they go a little crazy. At one point, Hal revealed that not only is he never unfaithful, he never even thinks about other women.
Their oldest son, Fancis ends up this way, and seems to have inherited his father's sense of devotion to his wife.
Married Single Other: The show didn't actually have a Happily Married couple - The original married couple Dickie & Babs had split up & moved on by the end of the series; whilst Eddie & Lillie are happily in a long term relationship, but aren't married. At least until the fifth episode, where they have a rush wedding after Lillie is diagnosed with a brain tumour. Naturally, she dies on her wedding day.
B.J. and Peg Hunnicutt. Having to be away from her led to a downward spiral of depression and a campaign of increasingly nasty practical jokes on B.J.'s part. A complete reversal from the characters they replaced, "Trapper" John, who despite being married slept with (or tried to sleep with) every nurse in the camp.
Sherman and Mildred Potter, which led to him becoming the father figure. And he's a career soldier who's fought in both World Wars and now Korea. Henry Blake, his predecessor, was a solid father to his men as well, but he was a womaniser.
Trapper sure did sleep around with nurses while in Korea, but his marriage might have been stable for he cared about his wife and their two daughters. His wife was very supportive in her letters; for instance, she absolutely backed him up when Trapper wanted to adopt a sweet Korean boy who was thought to be an orphan.
Medium: Allison Dubois and her husband Joe have a pretty stable marriage and three daughters. This despite the fact that whenever she has a prophetic dream, she ends up waking him up in the middle of the night.
Midsomer Murders: DCI Tom Barnaby and his wife Joyce have a pretty stable and happy marriage (unusual for a TV detective). She often gets annoyed when he runs off to follow up clues at a moment's notice, but it never seriously threatens their relationship.
No Ordinary Family: Jim and Stephanie Powell have their spats, but there's no denying their devotion to each other.
Phyllis and Bob Vance, Vance Refrigeration. For now, anyways. It's been heavily implied that Phyllis is cheating. Though it may be part of their kinky lifestyle, which includes: public sex, nudity at work, and goading flirtatious men into fistfights.
Once Upon a Time: Snow White and Prince Charming & Cinderella and her prince Thomas in the backstory. It's not only in the backstory anymore. The curse is broken in the season one finale and everyone remembers their true identities and all the couples are able to reunite.
One Tree Hill: Nathan and Haley James Scott. Yeah, they've had their ups and downs, but given they got married in the first season of a long-running soap-opera, while they were in high school, their long-term marital stability really deserves it's kudos.
Parenthood: The TV series adaptation has Zeek and Camille, Adam and Kristina, and (despite some occasional strains) Julia and Joel.
For all the ribbing he gets from his co-workers, Jerry has been happily married for quite some time- 28 years to his beloved Gayle.
Pushing Daisies: Ned and Chuck, the Official Couple, though they're not actually married - they couldn't be, as she's dead on paper. They verged on Sickeningly Sweethearts during Season 1; Season 2 has them transition from falling in love to being in love, as they learn to negotiate the rocky parts of couplehood. Little things, like he accidentally killed her dad with his powers. Or she tricked him into bringing her father back as a mouthy zombie. According to Word of God They have a long, loving relationship. Many, many years later they finally kiss when Ned is on his deathbed and Chuck hasn't aged a day.
Bert and Virginia have been together for 23 years after getting married as teenagers because of Virginia's pregnancy.
Jimmy and Sabrina, with Sabrina formally adopting Jimmy's daughter Hope as her own daughter. Sabrina's video diary reveals that while Jimmy thinks he's lucky to have met Sabrina, she comments that no, she's the lucky one for meeting Jimmy and his family. And despite all of their own insecurities, Jimmy and Sabrina deeply love each other and help provide a stable home for Hope.
Revolution: Aaron Pittman and his wife Priscilla before the blackout. He was a rich tech mogul who desired nothing more than giving his wife everything she could possibly want, unaware all she wanted was him. After the blackout, she proved this wasn't just an act by staying with him. But since he had no useful skills in a world without electricity, he left her behind with a group of survivors so he wouldn't hold her back. This is shown in a flashback in episode 6.
Ruby And The Rockits: Patrick and Audie Gallagher. In fact, it's revealed that they're passionately married, and frequently arrange to meet at home on their lunch breaks to spend quality time together.
Turk and Carla. Despite a few setbacks along the way, these two have been together since the first season and proceeded to get married and start a family, and seem to be quite happy together.
Inverted in the case of Dr. Cox and Jordan, who are happy together so long as they aren't married. It was only well after they thought they were divorced that they started a family and when they found out their original divorce was false, their relationship quickly broke down again until Perry decided to ask Jordan to divorce which quickly restored it.
From what we've learned in season 9, J.D. and Elliot seem to apply as well, and she's pregnant with their child.
Sanjay and Margaret (a.k.a. Ricky's foster parents) have the most solid relationship on the show.
Jack's mom and stepdad, Madison's dad and stepmom,Grant's parents, Dylan's parents, Leo and Camille and the couple who adopt Kathy's baby as well.
Smallville:Subverted with Lex who married three women in his life, first is due to meteor-power coercion, second end up with them trying to kill each other, and third end up with Lana Lang trying to kill him. Chloe and Jimmy also has a nasty ending.
Nearly every gangster in The Sopranos had a girlfriend on the side, which naturally led to some unstable relationships, but a couple were entirely faithful and seemed to have very happy relationships, most notably the sweet and loyal Bobby Baccala and the fiercely protective Johnny Sack, who once tried to put out a hit on someone who insulted his wife's weight.
Batiatus and Lucretia, bizarrely enough, considering that she repeatedly cheats on him with Crixus. Nonetheless, they seem to be deeply in love and totally devoted to one another in every other respect.
The cheating was Lucretia's way of giving Batiatus a child to make him happy, so even that shows how much in love they are, as Batiatus didn't said anything about it because he wanted her to have what made her happy in return.
Stargate Atlantis: Say what you like about Teyla and Kanaan's somewhat Ass Pull of a relationship, they are clearly very happy together, though not actually married, despite the fact that Teyla runs off risking her life every day and a psychopath wants to kill their baby. Those things would usually tend to strain a relationship.
Miles and Keiko O'Brien. They were both part of the crew on TNG and got married. They have a daughter together, and look like a happy couple with their fair share of problems, but they stick together.
By Klingon standards, Martok and his wife Sirella are happily married. Martok's speech about his marriage is one of the few heartwarming moments.
Martok: We are not accorded the luxury of choosing the women we fall in love with. Do you think Sirella is anything like the woman I thought that I'd marry? She is a prideful, arrogant, mercurial woman who shares my bed far too infrequently for my taste. And yet... I love her deeply. We Klingons often tout our prowess in battle, our desire for glory and honor above all else... but how hollow is the sound of victory without someone to share it with? Honor gives little comfort to a man alone in his home... and in his heart.
The mythical Klingon couple, Kahless and Lukara, that conquered heaven with their love in the wedding ceremony.
Sarek and his second wife Perrin appear in one episode. They are an elderly couple, and they look very much in love. Perrin is especially caring and protective of her husband.
Keiko and Miles O'Brian. The audience meets them when they are in a relationship and engaged. They get married and have a daughter together. They sometimes argue and have problems (like the one time when Keiko was transformed into her ten-year-old self). They are recurring characters and not that prominent, but their relationship is steady.
Step by Step: Frank and Carol start their new life together, and they stay a happy couple. They care about the other and their children, they love each other and lust for each other throughout the whole series.
Still Standing: Bill and Judy Miller. They're notoriously bad parents, but they love each other and they genuinely love their kids and try to do right by them.
John and Mary Winchester until everything goes wrong and it gets Subverted. It turns out that although they did love each other, their relationship was pretty rocky (with John actually leaving Mary at one point when Dean was a child), but that after she died John pretty much retconned their marriage in the minds of everyone except Dean, who remembers it.
Dean: Their marriage wasn't perfect until after mum was dead.
Bobby and Ellen in the post-Titanic alternate universe. (Like everything else on this show, the happiness is only there to make the inevitable more painful.)
There are quite a few happily married or mated Monster of the Week pairs. This is especially painful in contrast to the main characters, who can't hold down relationships to save their lives.
Bobby and Karen Singer before her death. And even after; briefly resurrected, doomed to turn into a mindless zombie, her biggest regret is causing pain to the person she loves.
Terra Nova: Jim and Elisabeth Shannon. They're committed to each other and their family, and a very good example of humanity amid dystopia.
The West Wing: Jed and Abbey Bartlet. note There was the time where he promised her he'd just be President for one term, and then decided to go for a second one without telling her first...and the time one of her old lies about his MS almost sunk the Congressional investigation into his nondisclosure...and the time she blamed his military decisions for getting their daughter kidnapped by terrorists... All in all, they were very happy given the kind of hell being President and First Lady puts on a marriage.
White Collar: Peter and Elizabeth have one of the most adorably functional relationships on TV. At one point, they get briefly snippy with each other about dry cleaning, which is viewed as the kind of catastrophe an affair would be in any other marriage.