Satoshi Hiwatari/Hikari and Daisuke Niwa in D.N.Angel may be heading this way after the series ends. Between the times they've saved each others lives and the magic they were caught up in it is impossible for them to not have some sort of tight relationship after everything, although the type of relationship is up for vigorous debate among fans...
Kyoya and Tamaki in Ouran Highschool Host Club Tamaki refers to himself as the father of the group and Kyoya as the mom. Kyoya doesn't seem to mind.
Kei and Yuri in Dirty Pair. (Though considering that they not only work together and socialize together, but live together and spend long periods of time alone together in deep space, as well as a few comments by their original creators, the "hetero" aspect is somewhat suspect. Some point to their relentless guy-chasing, which is a good point...if you believe in No Bisexuals.)
As one might imagine, this trope was inspired by the Dirty Pair Discussion page.
Their spiritual successors in that respect are Kiddy Grade's Eclair and Lumiere. From the same show, Dextera and Sinistra. Most of the other partners are either same-sex or... dubiously platonic.
Mobile Suit Gundam Wing: Most everyone came with a strong pairing: Trowa and Quatre, Trowa and Heero, Quatre and Heero, Duo and Quatre, and to a lesser extent Heero and Duo.
Natsumi and Miyuki from You're Under Arrest!. (Again, the creators seem to enjoy casting suspicion on the "hetero" part through various contrivances, including official art.) Although the plot is pretty clear about the guys they get paired with.
Mihoshi and Kiyone in Tenchi Muyo! (yet again, the "hetero" is somewhat in question.) This trope is somewhat justified by the fact that the two are stranded on Earth and struggling to support themselves financially; sharing an apartment seems like a reasonable fiscal decision, if one doesn't factor in Mihoshi's klutziness.
The variants in Magical Project S were a bit different. At one point, Kiyone was visualizing her future family with a handsome man, and one of the children was a dead ringer for Mihoshi! While Kiyone protests mightily, it looks more like a case of "She Protests Too Much".
Unless this is taken to imply Kiyone perceives a semi mother-daughter (or at least, older sister) relationship with Mihoshi, in that she has to take care of Mihoshi and watch out for her. Which would also fit.
Kiyone's Expy in the OVA series is more clear, treating Mihoshi exactly like a little sister.
Lupin and Jigen from Lupin III. Of all the gang members, these two are together the most and are even suggested to live together in several specials and films. Probably one of the oldest and greatest bromances in anime history.
A younger example would be Nagisa and Honoka from Futari wa Pretty Cure... They attacks work by holding their hands and they get stronger when they hold their hands stronger.
Rally Vincent and Minnie May in Gunsmith Cats. (Again, the hetero gets a little muddled, considering that in the first volume, May gropes Rally and comments on the firmness of her nipples after shooting a gun; at the end of the volume, Rally returns the favor, giving May a fairly extensive groping and going so far as to comment "they're like little pebbles".)
Also we later find out that May already had a lover that she's still holding a torch for.
The groping doesn't necessarily mean anything, and explained that the definition of 'private areas' in Japan is a little different than many other places. Friends (male or female) may well end up groping each other and commenting on what they feel as a joke.
Code Geass: Lelouch and Suzaku were this as children and try to be this in the first season of the anime (more evident in the supplementary material than the show, especially the manga where they are usually side-by-side at Ashford). This all goes to hell very quickly. By R2,however, they seem to be this again, as Suzaku is The Dragon to Lelouch's Big Bad and they are cohorts and allies.
In the alternate universe manga Nightmare Of Nunally, Nunally and Alice could be seen as this even though 1) Alice is Nunally's bodyguard and 2) the "heterosexual" part is suspect.
Yzak and Dearka are a strong example of this, especially in Mobile Suit Gundam SEED Destiny because some serious strings must have been pulled for Dearka to constantly stand beside the almighty Commander Joule the way he does.
Sven and Train in Black Cat, who travel around together as sweepers all the time, and adopt a "kid" (although they're not really daddy figures to her). Their Heterosexual Life Partnership is so strong that Creedtries to turn Sven into a monster so Train will join up with him instead.
Lampshaded in the anime, where a waitress notes that Sven is the father, Eve is the daughter, and...awkwardly skips over Train.
Ban and Ginji in Get Backers are the embodiment of this trope; even the other characters in the series remark on their "unbreakable bond". The resolution of the plot in the grand final arc of the manga actually hinges on the strength of their friendship. "The 'S' in Get Backers means neither of us is ever alone!"
Kazuki and Juubei. The anime attempts to make the 'heterosexual' part a bit suspect in order to attract a wider audience; but in the manga, they are definitely this.
Paul and Der Kaiser are also later revealed to have been this; with Der Kaiser even making Paul his son's godfather. Though they eventually end up going their separate ways, they still understand and trust each other completely.
Kirika and Mirielle in Noir. The "hetero" is a little suspect here, though. Not only do the two share the same bed, but in one episode, while staying in a hotel, they've apparently ''pushed the beds together''.
Later in the series, Chloe makes it very clear she seeks a lesbian relationship with Kirika.
Elenore and Margaret in Madlax do this to a lesser degree. Margaret being oblivious to the fact that Elenore is a lesbian, even right to the point where the latter dies later in the series.
Mai-HiME has (at least) two such pairs, Chie/Aoi and Haruka/Yukino being the most visible. Amusingly, both pairs eventually join Natsuki and Shizuru in the Mai-OtomeOfficial Couple pantheon.
Ah! My Goddess has Dai-Chan and Den-Chan (as they call each other), Keiichi's seniors in the Auto Club. Considering the cutesy nicknames and an apparent willingness to dress up in drag, this is again debatable. ...Just not as pleasantly so. Yikes, they're huge!
Most same-sex Digimon/Chosen Child partners will probably also be this (most explicitly in the English dub of Adventure when Izzy actually says he loves Tentomon). There'd probably be a lot more attention to this if Digimon wasn't built on the Children Are Innocent trope.
Goten and Trunks in Dragon Ball Z have been very tight friends all their lives and, as teenagers, quite often spill over into Ho Yay. Whether their being Fusion Dance partners makes this better or worse is debatable.
In the second Dragonball GT ending, it begins with all the various couples being shown together: Goku and Chi-Chi, Gohan and Videl, Vegeta and Bulma, Krillin and Eighteen...and then cuts right to Trunks and Goten walking along, in the same style. Apparently the creators consider them "life partners" after one fashion or another.
It's made worse by the fact that Trunks shows no interest in women, and indeed his mother has gone to the extreme of putting him in a office building shaped like a penis and filled it with hot women. He seems outright intimidated by both.
It's just been revealed that in the upcoming Dragon Ball Online, the two of them start a martial arts school together.
Can't forget Goku and Krillin, the original recipe version of what Trunks and Goten were later on. The two went from little kids to men in their fifties as best friends. In GT, Krillin is the last person Goku says goodbye to on Earth, even getting his wife and sons out of the way before one last spar with Krillin.
Dragon Ball Z Abridged lampshades this by making Goku frequently more concerned with Krillin's well-being than his son's.
From Dragon Ball to the end of Z (and GT, if you count it), Tenshinhan and Chiaotzu are pretty much always together unless the former is feeling especially protective. When it seems like Chiaotzu will be staying dead near the end of the Frieza Saga, Tien volunteers to stay in the afterlife with him without hesitation. Brought up in the abridged series.
Nanoha and Fate in Magical Girl Lyrical Nanoha. In the third series they share a bed, dedicate several hours before sleeping to "strategy planning and personal time" and adopt a Mysterious Waif together, having her call them both "mama". Yet they both refer to the other as nothing more than a "best friend" and are never seen doing anything explicitly sexual. Most likely an extreme case of Hide Your Lesbians.
The three are now called the Takamachi Family, according to the last Soundstages released; take that in any way you will.
Subaru and Teana still play this straight, though both are just as Ambiguously Gay as Nanoha and Fate were. The two first met in the academy when they were paired as roommates and training partners (as a result of being the only ones with custom-made Devices), and served together for their time in the Bureau until Mobile Sixth Division disbanded. They then went their separate ways to the Disaster Relief and Enforcer positions they always wanted (albeit with considerable reluctance on Subaru's part), but according to Teana, Subaru emails her so frequently she doesn't even feel as though she's gone.
Shikamaru and Chouji also fit the bill - being best friends without all the convoluted rivalry alongside it.
A late one that developed was Naruto and Killer Bee. Both being Jinchuriki, and the later helping Naruto overcome his self-hatred, and master control over the Nine Tails. The two developed a big friendship and helped each other for the majority of the War arc. The two even make a habit of fist bumping each other.
Johnny and Yosaku of One Piece, a bounty hunter pair who have the slightly hetero suspect position of following at Zoro's heels like lost puppies and idolizing him to a deeply heartfelt degree.
Also Jango and Fullbody, who are significantly less suspect in their enthusiastic joint pursuit of attractive female superior officer Hina. Although they do have a knack for breaking out into off-the-cuff, perfectly coordinated dance numbers.
Don't forget Coby and Helmeppo, introduced in the start of the series, and further shown several times later and in more recent arcs. The term Cobymeppo is coined in the titles of their own Lower Deck Episodes, helping to push these two towards Ho Yay.
Arguably Sanji and Zoro. Despite his obsession with women, he will drop everything to argue with Zoro. But they both respect each other as the two guys who anchor the crew.
Usopp, Chopper, and Luffy spend an inordinate amount of time together which made it all the more devastating when Usopp left. In regards to Luffy and Usopp, Luffy was able to recognize him just by his father's descriptions. It was also Usopp who motivated Luffy to continue fighting against Lucci
Zoro and Luffy have been with each other from the start. Zoro always understands what Luffy is about to do next without any words spoken. He's also the only crew member who never questions any order. Zoro even gave up his life and dream in exchange for Luffy's life when Kuma attacked.
The Straw Hats as a whole, really.
Shanks still see his relationship with Buggy as this, which is true no matter how much Buggy continues to deny it. Buggy, however, sees him as a sort of Sitcom Archnemesis, so it's best to identify them as Vitriolic Best Buds.
Ukitake and Kyouraku have been together since at least their academy days, which was a very long time ago. They're extremely close and have a reputation for being the perfect battle partnership, a fact that's even acknowledged by Yamamoto himself. Ukitake being badly injured in battle is also the only example of Kyouraku being willing to fight instead of trying to avoid combat like we've seen throughout the rest of the series.
America and Japan in Axis Powers Hetalia. They're on opposing sides during the WWII storyline, but are depicted as having become close friends in the modern-day strips and have virtually no Ho Yay moments between them despite being featured together in a good number of strips, in contrast with their more ambiguous relationships with England and Greece, respectively.
Spain and Romano, who always seem to be shown together in the modern-day strips. Though there might also be some Ho Yay going on there, what with Spain being quite fond of Romano at the very least and Romano being quite Tsundere towards him.
Lithuania and Poland act like this as well, although the latter pushes the definition of 'heterosexual' quite a lot.
Li Kouyu and Ran Shuei from Saiunkoku Monogatari. They are very rarely seen apart and attend social functions together, despite one being a scholar and the other being a general.
Many of the doubles pairs in The Prince of Tennis. (Some might be pushing it more towards Ho Yay: Koharu and Yuuji, maybe Ohtori towards Shishido and Eiji towards Ooishi.)
The instances in which Atobe Keigo is seen without Kabaji Munehiro somewhere nearby can be counted with one hand. To drive the point home, the fanbooks not only mention that they first met when Atobe was four and Kabaji three, but that Kabaji (and presumably his family) moved from England to Japan simply to follow Atobe.
Ryoma and Momoshiro. As the first regular Ryoma meets, the two are among the closest members of the Seigaku team. The only doubles match Ryoma plays in the series is with Momo, it's Momo who tries to help his best friend when he forgets how to play tennis.
Hakkai and Gojyo in Saiyuki. Word of God is that, while he technically owned the place and stayed there occasionally, Gojyo's house wasn't a home until Hakkai moved in.
Sanzo and Goku.
Plus they're all four of them all together all the time, with four-way attachments that mean they all feel unbalanced if they lose one.
Equally so in Gaiden, particularly Tenpou and Kenren, as Konzen and Goku's relationship goes more towards parent and child.
Arguably, Youji and Ken in Weiß Kreuz, to the extent that Youji warns Ken about the dangers of getting serious with a girl he's falling for - and, several episodes later, Ken returns the favor.
By the end of Weiss Kreuz: Gluhen, Ken appears to be well on his way to being Heterosexual Life-Partners with Aya, to the point that he follows Aya to England in Weiss Side B. When Ken explains his reasons for doing so, Aya hangs a lampshade: "...really like a naggy wife."
Ash and Brock from Pokémon appear to be life partners; they've been spending their time together for years.
Ash and Pikachu even more so, since they've been together from the beginning of the series.
In Ranma ˝ the most stable and enduring relationship of any of the cast is between Soun Tendo and Genma Saotome. In that series that really isn't saying much. Plus those two are stable old guys, helping with the 'stable' part.
Asakura and Sayo of Mahou Sensei Negima!, though for a change, it's the "life" aspect that's a bit questionable due to one of them being a ghost. The two have been practically inseparable after Sayo became visible to Asakura. They go on scoops together, get lost in the Magic World together, take baths together with Sayo's possessed voodoo doll resting between Asakura's breasts... And they are still together in the "Where Are They Now?" Epilogue.
Negi's father Nagi had 6 of those in form of his team, Ala Rubra. Not only he knew more than half of them since he was child (the youngest we see him is twelve and it looks like they already knew each other for years), they fought together in Great Magic War, which at one point could be described as "them versus the rest of the world" (they won), saved the world, and after that they traveled together for 10 years helping people. The only reason why they stopped was because he mysteriously disappeared 10 years prior to the beginning of the story. Nagi also formed pactios with both Jack Rakan and Albireo. So.
Mustang and Hughes in Fullmetal Alchemist. Academy friends, met up again in the Ishvallan War, and Hughes signed on to support Roy from below. Roy takes Hughes's death very hard, and goes on a psychotic rampage when he finds the perpetrator, Envy.
In Full Metal Panic!, an interesting example of this with a large age gap is Sousuke and Kalinin - though it was more so in their past history than currently in the series. As Kalinin put it, "Sousuke and I being inseparable seems to be destiny."
Gil and Oz in Pandora Hearts. In fact, their bonds are so strong that fans and characters in the series wonder if it's hetero at all. Especially on Gil's part. Word of God often plays up their guy love to reel in more fangirls.
Elliot and Leo also count as this.
Helen and Deneve in Claymore, although the "heterosexual" part is up for debate. At any rate, theirs is the longest-lived friendship amongst the protagonists, and Helen was the one who snapped Deneve out of her suicidal depression in their early days together.
In D.Gray-Man Mahoja and Anita are definitely this, as are Johnny and Tup (until THAT happens), and Reever and Komui.
Best Student Council has two such couples, Kanade and Nanaho plus Sayuri and Rein. Both groupings were brought together thanks to major events from their respective childhoods.
Judas and Luca of Saint Beast aren't really heterosexual, but they are very much the "best buddy/life partners" aspect of this trope. Goh and Gai can be argued to be this as well. In an aversion Rey and Shin, though having known each other as long as the other duos, are not as once they meet the others they largely gravitate away from each other despite maintaining their friendship.
Satoshi and Daisuke from D.N.Angel, although the Ho Yay angle is definitely played with in canon as well.
Huey Laforet and Elmer C. Albatross from Baccano!. The relationship just becomes more and more suspect as more of their backstory comes into the clear (Elmer, for example, seemed to have a tendency to make bets with himself to see if he could make Huey smile within a certain time period). And some of the quotes from Huey, such as the ones below, make him seem very Tsundere towards Elmer.
In the 'What do you think about Elmer C.Albatross' section of the novel, Huey said this in 1705, 'An annoying person. That nosy personality of his will just cause problems. I'm looking forward to when he dies.' but in 2002 he seems to have warmed up to him more and says,'He is...a close friend. Simply a close friend. No less than that, no more than that. Though it would be too embarrassing to tell him something like that.'
Mikado Ryugamine and Masaomi Kida from Durarara!!. They've been best friends since elementary school, and stayed in touch when Kida moved to Ikebukuro. It got to the point where Kida was practically begging Mikado to move to Ikebukuro to be with him. And despite Kida claiming they're in a Type 3Love Triangle with Anri, the two aren't any less close because of it.
There's also Simon and Dennis, who've stuck together for at least the last twenty years since joining The Mafiya together.
In Legend of Galactic Heroes there's Reinhard and Kircheis. Reinhard clearly perceives the extremely loyal Kircheis to be one of the two most important people in his life, the other one being his sister. This is up to Kircheis's untimely death protecting Reinhard from an assassination attempt. Reinhard changes greatly after that, becoming colder, with many characters commenting that a big part of Reinhard has died as well. Even then, however, Reinhard still consults with Kircheis, asking himself what he would do or say in a given situation, and favouring his dead heterosexual life partner's opinion higher than that of, oh, his WIFE.
In Gankutsuou, Albert considers himself to be Heterosexual Life Partners with Franz. The amount of Ho Yay on Franz's end, however, is so thick you could cut it with a knife.
Subverted by Rikimaru and Ranmaru of Kagerou-Nostalgia. They've been forced into this trope by The Big Bad they serve. As Ran used to be a girl that Rikimaru had a crush on. The whole thing's naturally played for angst.
Also, there is Meg and Jo from Burst Angel, although some clips can tell otherwise...
Vash and Wolfwood meet, bicker, and then seem to just...click somehow. They're the only people they know who can see through them so well, and also the only people they trust half as much to have their backs in a fight, and operate on incredibly similar wavelengths...they're best friends for life by the end of their second adventure together.
And this is despite them being one another's Foils and having profound philosophical differences, despite heaps and heaps of secrets, and despite Wolfwood being in the employ of Vash's Evil Twin all along. And in the manga, Wolfwood creepily seesaws between Crowning Moment of Heartwarming devotion and reflecting that Vash is sitting there with his back open and he could shoot him to death right now and get rid of half of the superpowered mutant threat to humanity...but eventually decides not to.
CLAMP have many examples of this to varying degrees of legitimacy depending on interpretation.
Tsubasa Reservoir Chronicle: Kurogane and Fay are the most recent of many CLAMP ambiguous couples. The two characters were designed to contrast each other in physical appearance, personality, backstory and clothing. Life partners status accentuated by Fay being forced to feed on Kurogane's blood to survive.
By the halfway mark of Tiger & Bunny Kotetsu has become the first and Only Friend Barnaby has had in his entire life. Despite already having a best friend (Antonio), by series end Kotetsu seems to have grown quite fond of Barnaby as well.
Lucky Star has Yutaka and Minami. While they do not consider themselves anything more than best friends, their friend Hiyori draws them in yuri.
Iris Zero: Mizushima Toru and Hijiri Shinozuka are best friends and confidants in each other. Even before Toru was involved with Sasamori, he established a bond with Hijiri after saving his friend.
Kuroko No Basuke Loves this trope. Namely with Kuroko and his buddy, Kagami. Though their heterosexuality has always been a topic of debate among fans.
Kaijou's Kise and Kasamatsu.
Midorima and Takao from Shuutoku.
Kagami and Himuro, also Kuroko and Aomine in the past.
Kiyoshi and Hyuuga.
Sakamichi No Apollon Does it with Kaoru and Sentaro, albeit that there may be times where the two may argue.
Rogue and Sting from Fairy Tail seem to be this. Their exact relationship hasn't been delved into, but they're at least significantly closer to one another than they are with anyone else in the human cast, in part because so far the only time they've been shown standing more than five feet from on another is when they've been required to split up for a tournament event.
Grizzly Bear and Shirokuma (Polar Bear) from Shirokuma Cafe have been friends since they were cubs. Grizzly has borne the brunt of Shirokuma's jokes and antics since then, but wouldn't trade their friendship for anything else.
In Dance in the Vampire Bund this trope is played straight with the Earthclan. Adult Werewolf warriors are always in pairs called Renri-no-eda which means "two branches intertwined, never to part." They are inseperable, and all Earthclan are male, but except for Angel's pretty explict affection for Akira none of the pairs seem romantically inclined with one another.
Another example is Princess Mina's relationship with Yuki which appears to be turning into this.
Oga and Furuichi from Beelzebub are this. While at the beginning it's less obvious, you learn more about the depth of their friendship as they continue to stick together. They may not look it, though, what with their constant bickering.