Alone On The Water uses this trope by name when talking about how difficult it is to define Sherlock and John's relationship. John remembers that Sherlock was amused when Harry referred to them as this.
In the pro wrestling story A Ring of Their Own, Ivory and Molly Holly are portrayed like this. Ivory is the one who convinced Molly to finally come out of retirement and wrestle again. When Molly won the FWF Championship, the first thing she did was hug Ivory.
In Empath: The Luckiest Smurf, Empath Smurf and Polaris Psyche are considered this, although Polaris is more asexual than heterosexual.
The first ten chapters of Sugar Rush Stories seem to exist specifically to make sure everyone is involved in this trope.
Touhou Ibunshu plays up Reimu and Marisa's canon HLP status for all it's worth (turns out Marisa isn't heterosexual though, but she ends up with someone else instead) and also adds Remilia and Sakuya, Yuyuko and Youmu, and Yukari and Ran, revolving much of the drama and heartwarming moments around their respective intensely close relationships. Kaguya and Eirin are not an example however, as they're Happily Married.
Daffney Unger has called MsChif her better half (half of The Scream Queens, their tag team). MsChif has in turn said she can make Daffney's ASS whole. (Unger was scouting for another member of her All Star Squad).
Edge and Christianaren't brothers in real life, as they used to be billed, but they have been best friends since the sixth grade. They went to junior high together, went to high school together, went to college together, trained for wrestling together, broke into the indies together, went into the WWF together... Christian's TNA stint is the first time in their lives they weren't around each other constantly. The second being Edge's retirement.
Matt Hardy and Jeff Hardy. Yes, they're brothers, but they're also a lot closer than most brothers their age would be; living within line of sight of each other, doing a webshow together, going out together, etc. They've built up a pretty substantial group of True Companions around themselves as well, with the rest of the OMEGA crew in close proximity.
The Miz and John Morrison during their time as a tag team. When they were separated in the WWE Draft, one announcer stated "The bromance is over!".
From TNA, the Motor City Machine Guns, who have used this exact phrase (specifically, Alex Shelley in regards to Chris Sabin) to describe each other.
Charlie Haas and Shelton Benjamin, aka The World's Greatest Tag Team, have a very strong bond with each other; Charlie has said in interviews that, sometimes, he thinks that his deceased brother Russ sent Shelton to him as a replacement.
Scumspawn and Satan to some degree in Old Harry's Game. Scumspawn has strong emotional love for Satan (not necessarily a romantic love) and Satan warms up to Scumspawn over time, mostly due to Scumspawn unwavering loyalty. In later seasons Scumspawn does talk about each other as though they're in a romantic relationship.
Warhammer has Gotrek Gurnisson and Felix Jaeger - originally kept together by a rashly-sworn oath on Felix's part when horribly drunk, but over the many decades of their adventures they have become pretty inseparable. Despite Felix's constant feeling that he'll never understand Gotrek's dwarfish psychology as long as he lives.
Ursarker E. Creed, Lord Castellan of Cadia, and Colour Sergeant Jarran Kell.
In a very strange and horribly twisted way, Warboss Ghazhgkull Mag Uruk Thraka and Commissar Yarrick, though it is only one way; Ghazhkgull regards Yarrick with as much affection and respect as any Ork can muster, especially for a 'puny 'umie', as a good Ork needs a Worthy Opponent. Yarrick, for his part, hates the Warboss with all his being.
Mame and Vera in Auntie Mame. The musical version gives them a duet about their relationship, "Bosom Buddies."
Avenue Q: Rod and Nicky, who are Captain Ersatzes of Bert and Ernie respectively. "We live together, as close as people can get / We've been the best of buddies ever since the day we met!" Which segues, just a song later, into "If you were gay / That'd be okay / I mean, 'cause hey / I like you anyway / Because you see / If it were me / I would feel free to say / That I was gay / But I'm not gay." Rod however had non-platonic, repressed feelings for Nicky.
Brick: Why can't exceptional friendship, real, real, deep, deep friendship! between two men be respected as something clean and decent without being thought of as— Big Daddy: It can, it is, for God's sake. Brick: -Fairies...
Enjolras and Grantaire from Les Misérables. This is somewhat more evident in the musical than in the book, probably because of how it's usually staged. When all the other students walk off with their girlfriends at the end of "Do You Hear The People Sing", these two leave with their arms around each other. The two were played by real life best friends, Ramin Karimloo and Hadley Fraser, in the 25th Anniversary Concert. Jason Forbach and Joseph Spieldenner, who play Enjolras and Grantaire respectively, in the US 25th Anniversary production are engaged.
MarkCohen and RogerDavis in Rent. Their duet, "What You Own" comes complete with Manly Tears and a big climatic Man Hug. The blink-and-you'll-miss-it instrumental reprise of "I Should Tell You" during their fight in "Goodbye Love" is also heartwarming.
Voldemort and Quirrell, at least, by the end. Senior Year takes it to the next level.
Harry and Ron in both musicals:
Ron: Favorite way to say "red wines" in a German accent? Both: Red Vines! Ron: (hugging Harry) Oh my god, where have you been all my life? Harry: In a cupboard under some stairs!
Estragon and Vladimir from Waiting for Godot. They have pet names for each other and put off killing themselves because of the slight possibility that one of them would live and be left alone. They were going to hang themselves so they could get erections. There is so much Ho Yay in this play, Wikipedia even has it's own entry on it.
Elphaba and G(a)linda from Wicked. Though how heterosexual they are varies, as some performances deliberately play up their relationship as a love story.
Lucentio and Tranio from The Taming of the Shrew. Tranio is "as secret and as dear" to Lucentio "as Anna to the Queen of Carthage was"note Refers to Queeen Dido and her sister from Virgil's Aeneid, and he'll do anything to help Lucentio.
A Year with Frog and Toad: Frog and Toad were always good friends in the original kids' books, but The Musical elevates them comfortably to life partners at the very least. They invade each others dreams to sing about how much they like each other. Twice. ("That's funny, you've been in all my dreams too...")
Katawa Shoujo has Hanako and Lilly. Hanako is an extreme social recluse, to the extent that she depends on Lilly just to help her cope at school, while Lilly has taken a role very similar to that of a mother in taking care of her. Their routes in Act 1 don't split until the very end, and each of their routes beyond that still feature the other heavily. In Lilly's route, Hisao comments that they're sort of like an odd family altogether, with him and Lilly as the parents and Hanako as the child.
Axel and Zexion in Ansem Retort. They're so close that Zexion was able to hit on Axel's wife-during their wedding-and not suffer a horrific death.
Arthur and Lancelot in Arthur, King of Time and Space. Which is... kind of awkward, in the circumstances, though it depends on the timeline. The "fairy tale" timeline strains their relationship the greatest, and they were never friends in the Mash parody line. The present-day and sci-fi timelines (especially down the road a few years) treat it as just a fact of their relationship - they both love Guinevere and each other too much to let it get in the way, and it's usually only a problem if someone else makes it a problem for them (like, say, political realities of their relationship or someone trying to reveal the queen is "unfaithful").
Rittz and Skip in Boxer Hockey have been friends since childhood and still live together.
Bumper and Stunt of Dominic Deegan - this has been noted by other characters in the series, often to tease Stunt, a staunch homophobe.
Black Mage and Fighter from Eight Bit Theater. So...Fighter McWarrior and Blackmage Evilwizardington have been travelling together for probably years. If Fighter's memory is to be trusted, they have been "best buds 4-eva" since when they were both kicked out of their respective schools, and in the epilogue continue to adventure together 3 years later.
Elliot and Tedd in El Goonish Shive, driven home by the fact that, in an alternate universe where Elliot was born a girl, they're dating. Later revealed by Word of God to be true in nearly every alternate continuity where they are both alive and sexually compatible. Which is probably why Lord Tedd is such a grumpy gus - no Elliot and no relief (his "Grace" is an extremely large (and male) squirrel hybrid by the name of General Shade Tail).
Emergency Exit has quite a few relationships like this, the most obvious being the main characters and roommates Bob and Eddie, as well as Karl and Jason even though Jason technically expressed romantic interest in Karl, but since Karl's straight they are only very close friends.
Gamma and Zimmy's relationship is simultaneously sweet and toxic: On the one hand, Zimmy would gladly die if Gamma asked her to; on the other hand, she poisons other people's friendships with Gamma to insure she never leaves. It really doesn't help that Gamma is about the only thing that keeps Zimmy from freaking out and bad *** happening. Word of God is that they are together, romantically but not sexually, but in the comic itself they're "only" this.
Annie and Kat, to the point that their relationship is frequently used as a symbolic representation of the harmony between the Court and the Forest. Not heterosexual however, as Kat and Paz start dating in Chapter 42 and Annie comes off more asexual than anything else.
Donald Donlan and James Eglamore. Surma noted in one flashback that when Jim was away for training, Donnie seemed to miss Jim more than she did. Surma was Jim's girlfriend at the time.
John and Dave, despite never meeting in person. The moirallegiance quadrant of the trolls' romance system combines this trope with elements of Morality Pet, though it's not restricted by gender at all and the most prominent examples are boy-girl.
Sakana: Jiro and Taisei have been best friends since middle school, and they are practically inseparable, go shopping together and share an apartment, and after Jiro finally goes on a date with cashier girl, Taisei can't stop worrying about him getting hurt, and so he stalks their date. The artist also stated that Shigeru and Taro are "bros for life", and it shows.
The main character 9 and his best friend Chuckles, in Serious Emotional Disturbances. Lampshaded at one point during a reunion scene with a Celine Dion song being played as the two run towards each other. So much that the town of Bum*** (where they live), including 9's evil Gramma, assume the two are gay for each other.
Torg and Riff from Sluggy Freelance. Though even after being best friends for decades, they're still not that comfortable with hugs. Zoe and Gwynn too, for that matter.
Terinu and Matt. They spent half their young lives together as the abused slaves as a pirate warlord, with Matt stealing food to keep Teri healthy and at one point he cuddled in bed with him after Terinu's powers were traumatically activated. Wordof God has stated "Both of them would rather be dead than see the other hurt."
Yu Han Sung: Since Ro has left, I guess I should fire you, too. Since you two are a set menu, like a hamburger and a cola. It would be inhumane to separate the two of you. I hope you continue your beautiful love forever and ever.
In CHKilroy and Beagle's series of intertwining ARMA 2 videos, they grow into firm friends and share for a while, a brotherly bond. The death of one causes the other to exclaim in despair, or even go into a kamikaze rage. In one mission Beagle accidentally proposed marrige to Kilroy, who said yes.
Jon and Arin on Game Grumps. These guys go together like salt and pepper, peanut butter and jelly, and any other heavy handed simile you can think of. Then they broke up, and Danny replaced John.
Homestar Runner's Strong Mad and The Cheat, and Bubs and Coach Z. Homestar and Pom Pom are supposed to be this, but in later cartoons it became much less apparent.
Alberta and Saskatchewan in the iammathewian project. Although whether there is evidence of it being a bit more romantic or not is up for debate.
Red vs. Blue: Grif and Simmons (and apparently, their voice actors in real life), and Tucker and Church to a lesser degree.
Dexter Gilligan and Lyle McDouchebag of Sanity Not Included. At least up until the end of Season 3, in which Lyle commits suicide in the animated section of the show, marking his departure.
Anthony Padilla and Ian Hecox of Smosh. Lampshaded at the end of the episode Replacement Needed; after splitting up, Anthony tearfully looks over a photograph of him pushing Ian on a swing, with the caption "Always and Forever...But We're Not Gay".
Survival of the Fittest: Jacob Charles and Ben Powell, or as their more affectionately known by the handlers, "BROMIES!".
Strippin, In The Little Wood and Sparkles* from Area 11 form this during their time as the "Dream Team", livestreaming together many times and clearly enjoying being with each other. Strippin also has this vibe with Benji, his collab partner from Rail Bros; Benji may not be part of the Yogscast, but they're very good friends.
Ben Stiller and Owen Wilson: The duo have collaborated with each other numerous times on-screen, and Wilson once said that Stiller was more defensive about Wilson's signature crooked nose than he was.
Conan O Brien and Andy Richter: Andy was a writer who was hired as Conan's sidekick to help him from being too nervous during the show. The producers had noticed that they had great chemistry, and they hung out so frequently that people started assuming that they were gay. When NBC executives demanded that Conan get rid of Andy, he refused. Andy's last episode of Late Night (before leaving to pursue an acting career) was one of only two moments wherein Conan cried on camera. There were also no guests in that episode, because it was all one big going away party for Andy. Andy eventually came back for the Tonight Show and stuck with Conan — angrily defending him from Leno and NBC — throughout the whole debacle. He hasn't left Conan's side since, and even off-camera, the two are still frequently seen together. It's widely known that every time Conan does something dangerous (like taunt an animal on the show to get laughs), Andy gets so concerned and angry that he refuses to talk to Conan for at least a day.
Kevin Smith and Jason Mewes (a.k.a. Jay and Silent Bob). Their friendship dates back to the mid-90s when Smith was working on Clerks, writing the part of Jay specifically for Mewes. Kevin has also helped Jason get over his drug addiction and they co-host Jay and Silent Bob Get Old to help maintain Jason's sobriety.
Laurel and Hardy were introduced on set of one of their earlier films and soon became best friends and became one of the most famous and most well-loved comedy duos EVER. After Hardy's death in 1957 Stan refused to ever work again.
Patrick Stewart and Ian McKellen: They met in old age, well after both became famous. They became tremendous friends, much to the delight of the general public. Co-starred as good friends turned mortal enemies Professor Charles Xavier/Professor X and Erik Lensherr/Magneto in the X-Men film series. McKellen is gay, Stewart isn't.
"I don't want to sound gloomy, but, at some point of your lives, every one of you will notice that you have in your life one person, one friend whom you love and care for very much. That person is so close to you that you are able to share some things only with him. For example, you can call that friend, and from the very first maniacal laugh or some other joke you will know who is at the other end of that line. We used to do that with him so often. And then when that person is gone, there will be nothing like that in your life ever again."
Stephen Fry and Hugh Laurie were definitely this during their A Bit of Fry and Laurie days, and arguably are to this day, despite not having worked together in any major capacity since then - although a "reunion interview" programme showed them picking up right where they left off, like tried-and-true pals. Although Stephen is openly gay he states that he has never felt at all attracted to Hugh, although he does admit Hugh to be genuinely handsome.