Ah! My Goddess: Keiichi and Belldandy are official from the very first episode because it was Keiichi's wish that she be his girlfriend forever.
Ai Yori Aoshi: Kaoru and Aoi get secretly engaged to each other right after the start of the story, but only Miyabi and Aoi's parents know about it. At the end of the manga they get married and live Happily Ever After, although Mayu claims that she hasn't given up.
Tatsumi and Mine become the official couple during the Wild Hunt story arc. Mine falls into a coma after saving Tatsumi's life, but he promises that he wants to make her his wife if he survives the final battle and she wakes up. She does and then he does.
Wave and Kurome. In chapter 64, she kisses him before going to her final duel with Akame, which makes Wave realize he is in love with her. Two chapters later, he arrives just in time to stop the duel between sisters, confesses his love for Kurome and declares his intention to abandon the empire to run away with Kurome and take care of her. After some struggle, Kurome accepts, they kiss and leave together.
Bamboo Blade: Dan (short and acorn-headed) and Miyako Miyazaki. The cast is still trying to figure out how this one works, although it helps Miya Miya is also a gag character who flips between sweet and psycho.
Rock and Revy of Black Lagoon are almost this, due to numerous... implications.
Bleach: Although the story focuses on a group of friends who fight and support each other, there is very little romance in the story and the only confirmed relationships tend to have one or both partners being deceased. These relationships only get revealed when they're relevant to the motivation of the main characters, such the back story of Ichigo and Ishida's living fathers and deceased mothers. However, the epilogue of the story occurs after a ten-year Time Skip and does reveal that several characters get together during that time. Ichigo and Orihime live together at the Kurosaki Clinic and have a son, while Renji (still Byakuya's lieutenant) and Rukia (a newly promoted captain) have a daughter.
Buso Renkin: Kazuki and Tokiko were effectively a couple by the end of the first arc and were together for the rest of the series. Even Gouta, the only other character with romantic intentions towards Tokiko, accepted that the pair belonged together by the end of the series.
Captain Tsubasa: Tsubasa and Sanae. They get married at the end of the World Youth Cup, and she's currently pregnant with their child.
Chivalry of a Failed Knight: Ikki Kurogane and Stella Vermillion, the protagonists from the aforementioned Light Novel/Manga/Anime, on a twist of what would be easily mistaken for an harem series by how it begins, the couple is formed very early on the story (around the end of volume 1 from the Light Novel, chapter 10 from the Manga and episode 4 of the Anime).
Rosette/Chrono and Joshua/Azmaria in the epilogue of the manga version of Chrono Crusade.
Sakura and Syaoran in Cardcaptor Sakura, who confessed to each other at the end of the series, as well as Real Syaoran and Real Sakura from Tsubasa -RESERVoir CHRoNiCLE-who also confess their love at the end of the series. The Clone Syaoran and Clone Sakura also married during the infinite time loop and Real Syaoran was apparently their son, and Clone Syaoran was cloned FROM the Real Syaoran, making the whole thing a LOT more complicated and confusing at times, but in the end the clones were paired together as were the real versions.
Fai and Kurogane, also from Tsubasa. They were so heavily hinted at that fans went crazy, bombarding CLAMP with questions and begging that they eventually said "Screw it!" and rolled with it. Took a few years too because they wanted to keep it ambiguous. Fans won out.
Touya and Yukito in Cardcaptor Sakura, and later in Tsubasa. Similarly, Gingetsu and Ran in Clover.
Other canon couples from Cardcaptor Sakura include Eriol and Kaho, Yamazaki and Chiharu and (manga only) Mr. Terada and Rika.
In both Tsubasa and Xxx Holic, Clow and Yuuko manage to achieve this status despite not appearing together in a single scene, not even in a flashback, and both of them being long dead. The major tipoff was learning that the only reason one half of this pair continued existing is because the other half wished for it.
Kamui and Kotori also count as an official couple, even though she dies later on. In fact, rather than any of the other couples already mentioned, these two appear on the 'the Lovers' tarot card included with the tankoubon version 
Nagisa and Tomoya are an official couple from the start: neither of them could imagine not being with the other one, and Tomoya doesn't even seem to notice that several other girls are in love with him.
The Kyou and Tomoyo Another World OVA episodes make Kyou and Tomoya or Tomoyo and Tomoyo the Official Couple respectively.
Cross Game ends with three of them: Nakanishi and his girlfriend from the track team, Ichiyo and Junpei, and finally Ko and Aoba.
Daisuke and Riku become a couple later in D.N.Angelalthough the series' manga still hasn't ended as it seems to be on hiatus again so it may end with different shippings later, but they seem to be canon at this time. In the anime they were also heavily implied to be canon by the end.
In DARLING in the FRANXX, we have Hiro and Zero Two. Even before the two confessed their feelings for each other in Episode 15, the evolution of their relationship and the challenges they face form much of the show's drama.
Detective Conan: The series is infamous for its tedious Will They or Won't They? shenanigans, and while there are a lot of canon ships in the series, it either takes tons of chapters to make them real or the readers/viewers are getting blue-ball'd again. However, some of them have managed to become official (already married couples excluded except one):
Subverted with Kogoro and Eri. They are technically still married, but they have an estranged relationship and it is only a matter of time when they are finally going to get back together.
In contrast to how long Shinichi×Ran or Heiji×Kazuha take to become a couple, Sonoko, who was notorious for frequently seeking a boyfriend, is together with Makoto Kyogoku the first to become an Official Couple. Initially, the Running Gag of Sonoko looking for boyfriends and having eyes for other good-looking guys still continued, but it toned down when their relationship became more and more serious, to the point that she would choose Makoto over her "sort-of-idol" crush Kaito KID.
Wataru Takagi and Miwako Sato are the first non-married police couple to become together and the cases involving their relationship have been frequently called "Metropolitan Police Detective Love Story". Nowadays, it's a Running Gag to tease their rather active sex life.
Ninzaburo Shiratori and Sumiko Kobayashi are one of the quickest ships to become together. Shiratori's previous crush on Sato is Retconned as him having mistaken her for Kobayashi-sensei all along.
Shuichi Akai used to be Akemi Miyano's boyfriend, but she is killed by Gin early on in the manga (or in episode 128 in the anime). Akai also used to be together with Jodie Starling prior to dating Akemi. He still has feelings for his dead girlfriend.
Zigzagged with Yumi Miyamoto and Shukichi Haneda. Shukichi is introduced as Yumi's ex-boyfriend, but he still has the intention to marry her. Yumi eventually catches on and supports him to fulfill his promise.
Shinichi and Ran finally become a couple in chapters 1004-1005, although they are still "separated" from each other since Shinichi has still not be fully cured.
Eureka Seven: Renton and Eureka are the two main characters and the main couple, whose relationship forms the backbone of the show. Holland and Talho's relationship in another major focus. Gidget and Moondoggie are the Beta Couple, and by the show's end Dominic and Anemone become a couple too.
And then there were Kyouka and Seilah, the two lesbian demons from Tartaros.
Aquarius and Scorpio, though no word on how they're progressing or if they can even still meet now that Lucy can't summon Aquarius any longer.
Zeref and Mavis, to the point where they're holding hands on the cover of Volume 53◊. It's also easily the most tragic Official Couple in the series, due to Mavis' "death" being what led to Zeref's Start of Darkness, because it was Zeref's love for her that killed her. Their relationship is more or less the focus of the Albareth Empire arc, due to Emperor Spriggan (read: Zeref) launching an invasion of Ishgal just to get his hands on Lumen Histoire (read: Mavis' physical body). It is also revealed that August from the Spriggan 12 is Zeref and Mavis's son and they never knew it!
The final arc subtly reveals that Gajeel and Levi have been in a relationship during the one-year time-skip and are sexually active. The epilogue makes a rather obvious hint that Levi is pregnant with Gajeel's child.
In the epilogue, Gray is starting to slowly accept Juvia's feeling towards him.
It is all but stated that Rogue and Minerva have been in a relationship or at least have slept with each other.
Fist of the North Star has Kenshiro and Yuria. Even after Yuria's death he remains loyal to her memory. And at the beginning of Kenshiro Den, the last of the Legends of the True Savior films, it's revealed that she is pregnant with his child, effectively retconning the entire Hokuto continuity after Raoh's death.
Many examples in Fruits Basket: Kyo and Tohru, Yuki and Machi, Hatori and Kana (later Hatori and Mayuko), Shigure and Akito, Hatsuharu and Isuzu/Rin, Hiro and Kisa, Ayame and Mine. There are also official couples for minor characters.
The main series has Hayato and Asuka, along with Beta Couples Shinjyo and Miki, Osamu and Clair and Shiba and Rena. The series ends with Hayato and Asuka's wedding ceremony with most of the cast attending it.
Shiba and Rena themselves are the official couple in the PlayStation game. The rest of the couples in the series are beta couples.
Shido and Madoka in Get Backers. Despite being the impetus of one side story and one major Story Arc, there isn't much to say about it beyond "it's cute," and "it works." Later in the manga, Hevn and Masaki.
Girls Bravo: Yukinari Sasaki and Miharu Sena Kanaka become this since the beginning of the series. At the end of the manga series, they get married and live Happily Ever After on Earth.
As of the Gundam Wing: Frozen Teardrop manga, Zechs and Noin, as well as Duo and Hilde are married, but in the latter case, they divorced later. The final page adds Relena and Heero as it ends with the latter proposing marriage to the former.
After War Gundam X has four final pairings (Garrod and Tifa, Jamil and Salah, Toniya and Witz, Ennil and Roybea) but at least two or three are pretty clear throughout the series and just need to evolve into full-fledged love.
∀ Gundam has a couple most notably Loran and Queen Dianna Soriel as well as Harry and Kihel Heim.
From Mobile Suit Gundam 00, the fourth and presumably final ED could best be described as an Official/Beta Couple montage, namely Saji Crossroad/Louise Halevy (the series' first couple since S1), Allelujah Haptism/Soma Peries, Lyle Dylandy/Anew Returner, and Setsuna/Gundam. The finale adds Patrick/Kati, wedding ceremony and all..
Hellsing: Pip Bernadotte and Seras Victoria. Word of God states that "if Seras wasn't a vampire and Pip wasn't a mercenary, they would be the perfect couple that everybody would be envious of".
High School D×D makes it clear that Issei and Rias are the official couple... and the rest of the harem would make it clear that's "official" as in "she gets to be the legal wife". Each member of the harem has a meaningful relationship with Issei, they're all okay with that, and any competition is for the position of First Mistress.
I'm Gonna Be an Angel!: Noelle and Yuusuke are an established couple already in the first episode, but fans tend to prefer Yuusuke paired with much more mature Natsumi. Also, Raphael and Mikael who in the last episode turned out to be the real main couple of the show, although they were established as a Official Couple from the moment Raphael appeared.
Inazuma Eleven: There aren't any official couples in the first series but Endou and Natsumi are married in GO (the sequel).
Inuyasha: Sango and Miroku, who have had a steadily evolving relationship from their mutual introductions. Interestingly, Inu-Yasha himself is part of a triangle (with Kagome and Kikyo). The manga finally resolves this issue by re-killing off Kikyo and giving her and Inuyasha a bittersweet closure so she can pass away in peace and he can let go of his guilt and be free to go with Kagome. In the Distant Finale Sango and Miroku have children and Kagome manages to return to the past to be with Inuyasha for good after some time spent stuck in the future.
Part 1 has Jonathon and Erina, who get married shortly before the end of the part.
Part 2 has Joseph and Suzi Q, who do likewise.
Part 4 has Koichi and Yukako, after the Cinderella arc.
Part 6 has Jolyne and Annasui in the form of their second universal reset counterparts, Irene and Annakiss.
Kaguya and Shirogane from Kaguya-sama: Love Is War are already heading this way by the time the story starts, and start dating in chapter 160. Technically they were sort-of already dating beforehand, but that was the point where the official love confession the series had been building up to took place.
Kimba and Kitty in Kimba the White Lion. Look, they're the only lion cubs in the whole series. It's pretty obvious that when they grow up, they'll marry and have kids.
Kimi ni Todoke: Sawako Kuronuma and Shouta Kazehaya. In the anime, it takes almost the entire second season to get them together.
KonoSuba: Kazuma and Megumin confess to each other in volume 9 and agree to become a couple in volume 12. They wanted to keep it a secret to not disturb the harmony in the group, but the confession of their friend Darkness towards Kazuma causes a reveal towards everyone else. And though they are still not quite lovers, they regularly cite their loyalty to each other as a reason to not get romantically involved with other people.
While not explicitly said to develop a romantic relationship in Magical Girl Lyrical Nanoha StrikerS, the Toy Ship of Erio and Caro does fit in the sense that, as the trope description states, both are overtly paired off and it seems understood by the cast that the two are an item. And their brief cameo in Magical Girl Lyrical Nanoha ViVid has them apparently sharing a flat together in World #61/Supools, and one of the Sound Stages has Caro actually following Erio into the men's side of a public bath to do some bonding — even suggesting that they take more baths together in the future — much to Erio's sputtered embarrassment.
It's strongly implied that the minor characters Griffith Lowran and Lucino Lilie have married between StrikerS and FORCE, as Lucino is introduced with Griffith's surname in the latter season. Their relationship is subtly hinted in the first StrikerS opening and in the StrikerS epilogue, and Shario noticed that there was more between them in the StrikerS supplementary manga.
Macross is usually good about resolving its love triangles:
Maid-Sama!: Chapter 57 establishes Usui and Misaki as an official couple. Even before then, it's obvious to everyone. At the end it's Hinata and Suzuna, Sakura and Kuuga, maybe Honoka and Aoi, Kurotatsu of the three idiots and Erika.
Mai-Otome switches things around a bit (thanks in part to Sitch Sexuality), pairing up Shizuru with Natsuki, Chie with Aoi, and Haruka with Yukino (the last two of which were subtexted heavily in the Mai-HiME anime).
Midori Days: Midori and Seiji. Pretty obvious when the story starts with them becoming literally attached to each other, which is how they stay for a majority of the 80+ chapter story.
My Bride is a Mermaid: Nagasumi and San. They got "engaged" at the beginning of the series and, romanticshenanigans aside, they're both committed to the other. So much so that, in one episode, Nagasumi gets upset at himself for even thinking about meeting with someone who sent him a love letter because he already has San, even though he was just going to turn her down (and it was a trick anyway).
My Monster Secret: Despite the occasional Unwanted Harem element, it's dead obvious from the get-go that Youko and Asahi are going to end up together. It's even clear in-universe; a few other girls confess their love for him, but in every case, they generally don't expect him to return their feelings, and only do it so that he can officially turn them down so they can all move on with their lives. Notably, even the author realized that there was no point beating around the bush, and gave them a Relationship Upgrade about halfway through the series, which then shifts its focus onto the effects of the upgrade on the cast.
Gendo/Yui is official in all versions of Evangelion (original or otherwise)
In the original series, Misato and Kaji count. Shinji and Asuka and Hikari and Toji could have counted, but unfortunately they never quite tie the knot. Though the latter is a clear Beta Couple, and even ends on a strong possibility of a happy outcome.
Ojojojo: Haru and Tsurezure hook up fairly early on (chapter 14). A cameo in Komori-san Can't Decline! implies that they got married after dating for four years (which was later confirmed when Ojojojo ended).
The only Official Couples in One Piece are minor couples who are married and even so, majority of the couples have one spouse either missing or dead. Some examples are Usopp's parents (mom dead, father a pirate) and Vivi's parents (mom dead, father still alive), Princess Shirahoshi's parents (mom dead, father alive), Rebecca's parents (mom dead, father alive) and Sanji's parents (mom dead, father alive). In Gol. D Roger and Rouge's case, they are Together in Death.
Ore Monogatari!!: Takeo and Yamato become a couple very early on (in the anime, it's the third episode) and about half of the series is about developing their relationship as a dating couple (the other half is about Takeo's bromance with Suna).
Otome Youkai Zakuro, spoiled from the start by both the opening and ending credits - Kei/Zakuro, Riken/Susukihotaru, Ganryuu/Bonbori&Hozuki.
Ouran High School Host Club: Chapter 81 of the manga confirms that the official couple is Tamaki and Haruhi. The anime, on the other hand, left things wide open for any shipping to possibly happen, particularly since Haruhi had had several meaningful moments with the twins, Kyouya, and Tamaki.
Ada and Vincent were one of these for much of the manga until the latter decided to end their relationship in the epilogue due to drastically differing lifespans and philosophies. In the epilogue it is also implied Ada ended up marrying some other man, albeit extremely vaguely. And there is also the incredibly ambiguous implication that she never got over Vincent.
Sakuta Azusagawa and Mai Sakurajima in Rascal Does Not Dream of Bunny Girl Senpai. It's made clear that no other girl will be able to interfere with this and even his first love wouldn't be able to get in the way of their relationship.
While only subtly hinted at in the manga, the Senshi/Shitennou were official in Sailor Moon Crystal version.
Samurai Deeper Kyo: Kyo and Yuya finally get together at the very end. There's also Kyoshiro and Sakuya and (in the anime) Benitora and Mahiro. You could also count Fubuki and Hitoki, but she is a Posthumous Character.
Sand Chronicles: Ann and Daigo. Then they break up for a nearly good 10 years, but get back together afterward.
Shaman King: Faust and Elisa who are Happily Married even though Elisa is dead Faust will join her as a ghost eventually, as well as Yoh and Anna. In the epilogue, it was heavily implied that Ren and Jeanne had a child together.
SHUFFLE!: In the anime, Rin ends up with his senpai Asa. Watching the recap seasonMemories makes it more clear why he chose her.
Slayers: The anime adaptation more or less cemented Lina and Gourry as an official pair since the end of season 2 when they share a kiss in another dimension. This was carried on to the original novels, where at the end, Lina expresses hope Gourry will marry her.
The official couples in Soul Eater are Kim/Ox and Marie/Stein, who are having a baby together.
Holo and Lawrence of Spice and Wolfopen a shop and have a child in the end.
WORKING!!: the first official couple is Oto-san and his wife Haruna, who he is searching for. The serie end with Souta and Inami becoming a couple, after she finally manage to overcome her androphobia and no longer punchhim. Yachiyo finally learn of and reciprocate Jun's feelings, and the Takanashi family's elder sister Kazue get back with her ex-husband Minegishi.
Yes! Pretty Cure 5: Coco and Nozomi. Really the only 100% official pairing within the rather large Pretty Cure franchise thus far. Every season has at least one highly probable pairing, some of which are basically accepted as canon. But Coco and Nozomi are the only pairing to have kissed, and Nozomi stated that she loved him in the final episode of the first season, among many other lovey-dovey things that certainly didn't happen with other (potential) pairings.
Though it presents itself rather like a harem, and the series is filled with Triang Relations, Yona of the Dawn has Hak and titular Yona as the official couple. In truth, the "harem" ends up functioning more as a found-family, and Hak's unrequited feelings do eventually become very requited.
The ending of season 3 cements Judai and Yubel, the franchise's only LGBT couple to date. note Yubel is an Intersex Duel Monster, putting Judai firmly in the pansexual category, and even In-Universe characters noted there was something off with Judai's sexuality.
Earlier in the same season, there's Amon and Echo. However, while Echo's feelings are very strong, Amon believes that achieving power is more important than Echo and he sacrifices her.
Yuri!!! on Ice has Yuri and Victor, who kiss in episode 7. As of episode 10, they are engaged.
Yusuke and Keiko, Sensui and Itsuki in Yu Yu Hakusho. Yoshihiro Togashi originally did plan for Hiei and Mukuro to be an official item as well, but severe fan backlash prevented him from doing so (although the anime implies it in contrast to the manga). In the first drafts of the series, Hiei and Kurama were supposed to be in a romantic relationship but Yoshihiro Togashi decided to leave them as close friends which would explain all the Ho Yay between them.
Teasing Master Takagi-san has Nishikata and the eponymous Takagi. While Nishikata spends a big part of the series trying to outsmart Takagi in any prank (only to be outsmarted instead by her), and resorts to all kinds of Suspiciously Specific Denial and She Is Not My Girlfriend answers when he's told by someone that he likes Takagi, it is made clear that they really care about each other. And as revealed in a Time Skip chapter in the manga, they will eventually marry and conceive a daughter.