In Fullmetal Alchemist, Hughes has this kind of extreme affection for his wife Gracia and his daughter Elicia, but perhaps atypically, it makes him really likeable rather than annoying. It helps that he's a pretty BadassKnife Nut.
Not to mention he takes his adoration for them to extreme levels, to the point of shoving pictures of his daughter in his (overworked) subordinates' faces and expecting "her adorable face" to replenish their energy. Yeah.
Sig and Izumi Curtis (of all people) are so lovey-dovey that they traumatized Ed and Al when they were kids. They hang on each other, invoke sparkly backgrounds, had a Meet Cute involving a bear carcass, and frequently kick ass together while cooing at each other. Go figure.
Chet and Addy in Haré+ Guu. Even the romantically-minded Marie refers to them as "Chetttttt" and "Addyyyyyy".
It's mentioned that every once a Month Adi gets into a fight with Chet over the stupidest things. But always gets back together with him after he says some sappy line.
Kazuya and Akane at the end of Mai-HiME, possibly to balance that out their counterparts put in an impossible position in Mai-Otome.
Umi's parents in Magic Knight Rayearth are more than Happily Married. They take any excuse to fawn and coo all over each other. Even Umi herself is thoroughly disgusted by their incessant, diabetes-inducing displays of affection and refers to it as "the perpetual honeymoon".
Tokyo Mew Mew: Ichigo's parents couldn't be lovey-dovier if they tried.
Hayashi and Morimoto from Godannar seem to exist only for comic relief and to annoy characters with less-than-perfect relationships. At least until the Distant Finale, where Hayashi is revealed as Chekhov's Gunman
Just to make it clear, they're both utterly bug-duck crazy: Mika was Seji's stalker until he took a baseball bat to her skull for finding a decapitated head when she broke into his apartment. She got plastic surgery to look like Seiji's true love, making Seiji think Mika was said true love, and they got together. Then the truth came out, but the pair are so crazy they stick together anyway. Oh, and Seiji's true love was said previously mentioned decapitated head, which his incestuous big sister got rid of because she wanted one less rival for her brother's affections (but that's another story)... Did we mention they were crazy yet?
Michi and Yoshirin, the young couple from Crayon Shin Chan, are a clear parody of this trope. Apart from occasional (and pretty dumb) break-ups, all they do on the series is be lovey-dovey with each other. At least on the original and Spanish dubs.
Yuuki and Yume from Kanamemo, and not even Yuuki's jealousy or Yume's ditziness can put any dents in that.
In a different episode, Ranma and Akane pretend to be this type of couple to get Ukyo out of the Tendo household. Unfortunately for them, they've made a habit of arguing and find being lovey-dovey with each other a daunting task. But hey, it makes for good television!
Ayano and Shimotakatani from High School Girls are constantly like this, to the disgust of Ayano's boyfriend-less friends.
Himeno's father Kaoru and her (very wealthy) stepmother Natsue from Prétear, to the embarassment of their daughters.
Yukio Ayashiro and his wife Noriko in a two-part episode of Detective Conan. It's a little more justified as they had just gotten married, tho. Their old friend and the local Private Defective Kogoro openly lampshades the trope:
Katsuo and his wife in Yakitate!! Japan. Their cutesy gushing only helped to encourage Kuroyanagi to eliminate Katsuo in the semi-finals of one Tournament Arc.
Eureka Seven: Count the times Eureka and Renton argue with each other, come on. That's right, 1. They argued once in a 50-episode show. And that scene lasted shorter than 1 minute.
Uranborg and Arkangel from the BL manga "Yasashii Ryuu no Koroshikata" after their Relationship Upgrade. Most of it is Uru constantly fawning over Ark, declaring his love and unending devotion to his "pledged one", especially after they get together. When Ark finally reciprocates, he eats Uru's words up like candy when he isn't getting shy over it. Take a look. (Warning: Spoiler.) 
Apollo and The Midnighter from The Authority, surprisingly. They're very affectionate but will still rip out your spine if you make one of them mad and god forbid you actually harm one of them or their adopted daughter - you will wish you had never been born.
Hourman and Liberty Belle in Justice Society of America. Thankfully, the lovey-dovey stuff doesn't get in the way of them kicking ass in battle.
"Richandamy" from the comic strip Zits are a high school relationship taken all the way to symbiosis.
Amusingly, Richandamy were based on two college friends of creator Jim Borgman. They were actually named Rich and Amy, he was tall and she was short, and they practically were that inseparable. They're now Happily Married with three kids.
Peter and Denise of Foxtrot were known to be like this from time to time. One occasion featured them in a rather sweet moment, in which Peter talked about how unbelievably great it was to finally have a girlfriend like her. "Just great?" she responds. "Okay, super-duper-ooper-great." "You're so cute." And of course Jason and Marcus are spying on them behind a clump of bushes, causing Jason to whisper: "If I'm ever that cute, shoot me dead."
One dialogue from Empowered: "No, you should wear that outfit (tee hee)!" - "No, you should wear that outfit (tee hee)!" No wonder the Caged Demonwolf imagines a scene with better dialogue, in his usual flowery style.
In Monica's Gang: in the teenage spinoff, Monica and Jimmy Five abandon their normal personalities of Tsundere and Jerk with a Heart of Gold and become one of these when they finally start dating. This ends up disgusting the other characters so badly that many of them start to root explicitly for the breakup of the couple.
Barbie and Ken from The Sandman. They wear matching outfits, finish each other's sentences, and always have an arm around the other. This appears to be a facade on both their parts. We later get to see their most personal dreams and it's revealed that nice guy Ken dreams of sex (not with his wife), money and power, while the shallow Barbie is seen dreaming of adventure and bravery.
Will Vandom and Matt Olsen in W.I.T.C.H.. Usually the others take it in stride (especially Cornelia, who sometimes is almost as bad as them), but a particular accident in the New Power saga caused them to have faces the readers can't tell if they're moved or sickened (with Hay Lin verging on laughing herself silly).
Winsor Mc Cay had a couple like this in one of his early minor features.
Spoofed in the movie The Naked Gun 33 ⅓: The Final Insult. While at marriage counseling, Frank and Jane start calling each other sappy pet names. At first the therapist smiles at the display, but after a few more he says "Mr. and Mrs. Drebin, I'm a diabetic. I think you two ought to go now."
Googly-Bear and Schmootzy-Poo (aka Mike and Celia) in Monsters Inc.
In The Mummy Returns, whenever Evelyn and Rick kiss, they'll get a disgusted look and the "Find yourself a room" comments from their son and/or Evelyn's brother Jonathan.
In Antz, Chip and Muffy (the Cultural Posturing wasps). Chip is referring to Muffy as "Cuddly Widdles" and "Wattling Kiddles".
Barbie and Ken from Toy Story 3. Buzz makes a "you have got to be kidding me" facial expression after overhearing a conversation between them.
The pair of robbers (Amanda Plummer and Tim Roth) at the end and beginning of Pulp Fiction are this. They're even credited as "Pumpkin" and "Honey Bunny."
Parodied in Chitty Chitty Bang Bang in the song "Chu Chi Face." (And you're my teddy bear. Together we're a Chu-Chi Woo-Chi, Ooo-Chi Coo-Chi Pair!) Of course, the entire time the Baron and Baroness are singing this to each other, he's trying to arrange an untimely death for her, resulting in her getting more and more nervous and uneasy as the song progresses.
There's a character (Manilov) in Gogol's Dead Souls who shares with his wife a sickeningly sweet affection.
"...if Ron was going to begin calling her 'Lav-Lav', he [Harry] would have to put his foot down."
Bill and Fleur fit this trope as well, especially if you ask Ginny and Hermione.
When contemplating the idea of Ron and Hermione getting together, Harry fears (among other things) that they might turn out like this, using Bill and Fleur as an example.
Parodied in one of the JW Wells And Co novels by Tom Holt, where a bickering couple are tricked into overdosing on love potion. They start using pet names at the end of every sentence but retain their normal personalities, leading to sentences like, "Don't be such a bloody idiot, honey-bunny".
Every vampire couple. The only human couples worth mentioning are either broken up (Bella's parents, Jessica and Mike), basically nonexistent (Angela and Ben), or barely begun by the end of the series (Charlie and Sue Clearwater).
The werewolves and the girls that they imprint on. To the point in which the other wolves in the pack do not look forward to mindlinking with a wolf who had just been visiting his imprintee.
In the second book of the Guardians of Ga'Hoole series, the Band comes across a pair of owls that do not give their names but refer to each other as Sweetums and Swatums. They preen each other and talk about eating sugar gliders while speaking to the group.
In Salman Rushdie's Haroun And The Sea Of Stories Prince Bolo and Princess Batcheat are like this, to the disgust of absolutely everyone around them. Bolo is so oblivious (and stupid) that he constantly praises the silly Batcheat for her beauty and her singing voice, both of which are described in detail as completely horrendous.
Tales of Kolmar: As newlyweds, Lanen and Varien are like this, with Jamie even hanging a lampshade on it and them teasing each other about trying to tone it down in front of him. However, they do find difficulties, pains and sorrows and arguments that can't be soothed away with a touch or a few words, and eventually the relationship smooths into Happily Married. They still get silly sometimes, but Lanen notes that their bond is more complex now.
The Hunger Games: Katniss and Peeta sometimes make use of this trope to sell their (maybe not entirely) fake romance to the Capitol audience.
In Smallville, Chloe and Jimmy could be this on one of their good days. Just look at Clark's expression whenever he walks in on them kissing. In one episode, it's mentioned that Lois—who was then-currently living with Chloe—wants to move away solely to get away from their constant lovemaking, noting that it's just extremely awkward when she hears them through the walls. In another episode, poor Clark walks into their apartment and finds evidence of their, um, hobbies lying around.
Also Clark and Lana on one of their... er, bad days?
The "Soup Nazi" episode of Seinfeld where several of the characters in relationships had a sort of competition to be the most sickeningly sweet.
"You're shmoopy!" "No you're shmoopy!" George to Elaine: "I had to listen to them for 15 minutes arguing over which one of them was 'Shmoopy'."
An episode of Caroline In The City had Caroline sitting in a diner waiting for a friend, and being forced to sit through a couples wuvvy-duvvy baby talk and nicknames for each other. When her friend finally shows up, she asks, "Who are they?" Caroline responds, in total deadpan, "Billy-Bear and Cindy-Doodle. Satan sent them."
One episode has Barney and Abby (Britney Spears) pretend to be a couple like this in order to make fun of Ted. Barney then proposes to her, but he thought it was part of the act and she thought it was for real.
When Ted and Robin were going out, they got Barney to do what they wanted once by threatening him with sickeningly sweet behaviour.
Lily and Marshall occasionally lapse into this. For example, their pet names for each other are "Lilypad" and "Marshmallow". They share food and like wearing couples' costumes for Halloween.
When Ted and Victoria started going out, it got to the point where Marshall and Lily were jealous of how lovey dovey they were.
Danny and Lindsay on CSI: NY have been accused of this on occasion because of the back and forth comments and occasional flirting that come out when they're working together.
Niles and Daphne were like this for a while after they finally got together. If you spend seven years pining after one girl, you're allowed to be a little obnoxiously happy, the other characters was greatly relieved when the two got over this phase.
A later episode in the last season also has an interesting P.O.V based example; at one point, both Martin and Niles — both of whom are in happy, stable relationships, Martin about to get married again and Niles married with his first child on the way — sigh about how happy they are. From their perspective, it's merely a content but throwaway musing. Frasier, however, happens to be going through a particularly dismal time in his already pretty grim love life, so from his point-of-view, Martin and Niles are being insufferably smug and sneering about their good fortune.
Lilly and Oliver in Hannah Montana, after being friends since kindergarten, suddenly turn into this, even calling each other "Lilypop" and "Ollypop".
Buffy and Spike, when one of Willow's accidental spells made them want to get married, treated each other like this.
True Blood: Hoyt and Jessica in Season 2, until after enduring hours of abuse from his mother, Jessica quite justifiably snaps and snacks on Maxine's juicy jugular, thereby pushing Hoyt's Relative Button.
To a lesser degree, Sookie and Bill.
In the "Howling Wind" episode of Cirque du Soleil's Widget SeriesSolstrom, a newlywed couple is soooooooooooo in love with each other that neither notices that the honeymoon hotel they've just checked into has been magically transformed into a Gothic Hell Hotel. In the end they become happily-in-love vampires.
Sweets and Daisy from Bones. She calls him "Lancelot" (his first name is at least Lance, so it's an understandable nickname). They're going to get married. Maybe that'll calm them down. I doubt it, somehow. It still makes you smile, even as you're trying not to vomit, because they're so matchingly dysfunctional.
Daisy: Bye, Lancelot! Colon, end bracket, colon, capital D!
Sweets: Semi-colon, end parenthesis, less than sign, numeral 3!!
A couple in an early episode of 7th Heaven was this trope personified until the husband confessed to his wife that he'd never properly divorced his first wife. Much angst and screaming ensued and it was up to Eric to save the day.
On an episode of Everybody Loves Raymond, Ray and Debra go to Vermont to stay at a bed-and-breakfast for the weekend, and end up across the hall from a sickeningly sweet couple (who have only been dating for 6 weeks) who can't stop giggling and making sexual innuendos at each other. Ray and Debra stare in disbelief at this behavior. At one point, Ray and Debra are outside their room, when they hear the other couple (thanks to their obnoxiously loud giggling) and actually rush to find their keys to get into their room before the couple can turn the corner and talk to them.
In another episode, Robert and Amy are acting like this shortly after getting married, which Ray and Debra don't mind too much — until Robert and Amy start giving Ray and Debra marriage advice. Ray and Debra, who have been married for over a decade, don't appreciate getting advice from newlyweds (or in Ray's words, from "the guy who married a stripper, then divorced a stripper, then married a regular person, then hung in there for three whole months"), and feel that Robert and Amy are being presumptuous, though Robert and Amy point out their observation that Ray and Debra really don't seem very happy most of the time. Then, the entire party is lectured by Marie and Frank, who—despite often butting heads—genuinely enjoy the witty back-and-forth between them; it's hinted that, despite the fact that Frank and Marie are definitely not this trope, they may actually have a happier and healthier marriage than either Robert and Amy or Ray and Debra, due to their complete honesty with one another and their mutual enjoyment of their back-and-forth. For Frank and Marie, the verbal sparring is a game, and doesn't detract from the fact that they really do love each other.
Phoenix plays one-half of this equation in the first case of Phoenix Wright: Trials And Tribulations. Too bad for him that his sweetheart isn't anywhere near as into him as she pretends. Okay, maybesheis...
A mod to Baldur's Gate 2: Throne of Bhaal adds a character who seeks out romance with Imoen. In one memorable exchange, they use so many consecutive pet names for each other that even the good-aligned party members find themselves tempted to agree with Sarevok's comment: "Say the word, and I will kill them both. Please."
If like me you were ready to hunt across the Internet after reading that, it's kelsey.
Pokémon has several of these couples, who would constantly talk about "lovey-dovey" they are. For some creepy reason, they were often found in places like graveyards and abandoned ships.
Happily Married couple Maeda Toshiie and his wife Matsu from Sengoku Basara. On one occasion Toshi came to Matsu's rescue on the battlefield, and they shared a tender moment together, leaving their opponent Yukimura at a complete loss of what to do.
In Tales Of Hearts, Shing and Kohak. Other party members occasionally complain about it. At one point Hisui and Beryl actually raise their Relationship Values through their mutual annoyance at the main couple's sheer couple-ness.
While playing their mini-games in Majora's Mask, you actually get the option to shoot them to increase your time limit. Much fun! And if you win, they say "That's annoying, so let's show off even more!"
If you help two Dalish elves get together, they begin acting like this, while Morrigandisapproves.
"Does anyone else feel the urge to vomit? No? 'Tis just me?"
Harvest Moon couples have a tendency to be Happily Married, but the award for soppiest couple in the series probably goes to... Jake and Colleen, Maya's parents in Tree of Tranquility and Animal Parade. Jake compares everything to his beloved Colleen and absolutely lives to spoil her, at one point even using the Wizard's crystal ball to read her mind to find out exactly what she wants. They're also constantly holding hands and cuddling. This probably explains why Maya is The Cutie—spending all her life around that kind of sappiness, what else would she be?
Sims with a high mutual long-term attraction will get completely soppy in the presence of their loved ones. Spontaneous serenades and leaping into each other's arms is cute the first time. The 18th time in a row, not so much.
"At least they're not one of those sickeningly cute couples. Just sickening."
Cho and Cedric acting like this in A Very Potter Musical piss Harry off to no end since he has a crush on Cho. It actually doesn't end well though since Cedric gets murdered.
The Lizzie Bennet Diaries: Jane Bennet and Bing Lee when they start dating. She bakes him home-made cookies. He watches romantic period drama with her and treats her like a princess, pretending to carpool when he in fact just keeps giving her a lift. Lizzie is happy for them, but she implies that sometimes they're too much to take and also that Jane has the "I-want-you-to-be-in-a-happy-relationship-like-myself" vibes which make her uncomfortable.
A featured couple in Futurama who ran the candy company Romanticorp.
And from I Dated a Robot:
Lucy Liu-bot: You're cute! Fry: No, you are! Lucy Liu-bot: No, you! Fry: No, you! Professor Farnsworth: Oh dear! She's stuck in an infinite loop, and he's an idiot! Well, that's love for you.
A both odd and hypocritical version of this appared on Kick Buttowski with Ronaldo witnessing a kissing "couple".
Ronaldo: (while talking on the phone) "Oh, just a second, honey..." (yells at kissing couple beside him) "YOU KNOW THERE IS SUCH A THING AS TOO MUCH AFFECTION!" (goes back to his phonecall) "See you soonsies!"
The couple in question were of course... Kick and Ronaldo's girlfriend (whom he was talking with on the phone), Kendall.
Clover and Blaine have this type of relationship in the final season of Totally Spies!.
Although not a complete example of this trope, there is one episode of My Life as a Teenage Robot in which Brad is about to be married to an alien who refers to him as "Bradley-Boo". Squick.
Professor Utonium and Miss Keane become this in an episode of The Powerpuff Girls. They break up when it turns out that he doesn't like her cat.
Big Macintosh and Cheerilee act like this in the My Little Pony: Friendship Is Magic episode "Hearts and Hooves Day", thanks to a love potion provided by the Cutie Mark Crusaders. They spend nearly half the episode staring into each other's eyes and calling each other cutesy pet names.
The "sickening" part is quite literal, they visibly sicken the Crusaders repeatedly with their cutesy pet names.
Big Macintosh: SHMOOPY DOO!
Hugh and Jean in Taz Mania, at times. Taz and Drew certainly seem to think so.
In-universe example in Young Justice with Lagoon Boy and Miss Martian
The Legend Of Korra: Mako and Asami are this way for a time, although they're not as bad as some of the other couples on this page. Korra is especially disgusted when the two of them Eskimo kiss or wink at each other and blow kisses from across the room.
Mako: These new uniforms look great!
Asami:You look great, champ!
Episode nine is about when they start moving away from this type of relationship, as they eventually break up and turn into good friends instead.
The Adventure Time episode "Dream of Love" had Tree Trunks and Mr. Pig making the candy kingdom sick with their constant displays of affection.
On The Simpsons, Ned Flanders and his wife frequently verge on this territory. At a marriage counseling group-therapy retreat, Ned reveals the sordid truth that "Well, sometimes she highlights passages in my bible instead of her own!", to which Homer rolls his eyes and says, "It's a good thing you don't keep guns in the house!"
You might know at least one couple like this.
You might be half of a couple like this. Glad you're happy but maybe go be happy about ten or twenty feet farther away.
There's always at least one showmance like this in a theatre production. To everyone involved, it's a distraction.
Subverted in the Behind The Music episode about TLC. When Left Eye was dating football player Andre Rison, her bandmates would get annoyed by their sappiness. T-Boz mentioned how they'd always call each other baby: "Hey Baby... Baby... Baby..." and it segued straight to Chilli, interviewed separately, saying the exact same thing. Two years into the relationship Left Eye burned his house downnote Admittedly, it was an accident. She had previously burned a teddy bear collection in the same bathtub after a previous fight, and assumed that her current victim (a pair of woman's sneakers that weren't her size) wouldn't be any worse. However, what she didn't realize was she had damaged the previous (marble) tub so badly, it had to be replaced with one made of fiberglass, which got out of control much faster. when she thought he was cheating.
This installment of Gothic Charm School provides some useful tips for dealing with people like this.