Franklin: Bear and Franklin; in fact, on the former's side, he Ambiguously Gay spends most of his time exclusively with Franklin.
Teen Titans: Beast Boy and Cyborg. Or, alternatively, Cyborg and Robin. Also, Starfire and Raven.
Wild Kratts: The Kratt brothers, on all four of their shows. It's magnified when they get excited about their work and become obnoxious together.
The Backyardigans: Pablo and Tyrone. As one official web page put it, "Any problem that Pablo can imagine, Tyrone can solve." They are best friends, and on those grounds, Tasha and Uniqua also count as an example.
In Arthur, of all the show's characters, Arthur and Buster represent this the most as they hang out and interact with each other more than most of their classmates and family. The complexity of their friendship becomes deeper when the episode Arthur's Faraway Friend kick starts an entire sub plot where Buster moves away to travel with his dad, leaving Arthur behind and having him living life without his best friend. Needless to say, it's a pretty sad episode in an otherwise upbeat kid's show.
In fairness to Buster, he has only his mother for company at home. Sometimes Arthur invites Buster along when traveling, as well.
Darkwing Duck and Launchpad McQuack. Darkwing called Launchpad his "sidekick", but the dynamic was different. There's even less explanation for his living in DW's civilian house, plus Launchpad didn't even bother with a Secret Identity.
Following the series' return, Stewie in Family Guy seems to have abandoned his plans for world domination just to have more time to hang out with Brian, formerly his arch rival. "Brian & Stewie" even has them admit that they love each other as friends.
Given that the founders of Hanna-Barbera started out making a series about enemies that are sometimes buddies and formed a whole studio of their own, this shows up a lot within their shows to the point it's actually one of the charming hallmarks.
And, in what can only be seen as a further connection, when two men who met at HB formed their own sister studio Ruby-Spears, this trope still continued on through that studio's output as well
Mac and Bloo from Foster's Home for Imaginary Friends. Never mind the fact that Bloo is a figment of Mac's imagination... Although, to be fair, most of the supporting cast are figments of the imagination. Back to Mac and Bloo, Mac has made a deal with Mrs. Foster to meet with Bloo everyday. It's even a plot point in some episodes.
Ren and Stimpy are a textbook example of the trope Depending on the Writer. In the ill-fated revival series that briefly ran on Spike TV, Ren and Stimpy were actually a gay couple. Word of God says that their status depends on which is funnier for the specific episode, and the extent of Ren's contempt towards Stimpy seems to vary Depending on the Writer. Especially in earlier episodes, they're portrayed as a fairly normal pair of buddies, with little venom coming from Ren. Some episodes of Adult Party Cartoon show their relationship as a borderline type 1 of Vitriolic Best Buds (like "Stimpy's Pregnant"), while others make Ren out to be rather tender and kind-hearted towards Stimpy ("Onwards and Upwards"). It happens in the original series too, though much more subtly ("Rubber Nipple Salesmen" for the first example, "Son of Stimpy" for the second).
Stan: I don't wanna hang out in the kids' room. I won't know anybody. Randy: Well, it would be good for you to make new friends. You can't just hang out with your buddy Kyle all the time. People will think you guys are, you know, funny.
Especially in the Guitar Hero episode.
Kyle: Don't you get it? I don't need you anymore! Stan: I know. I need you.
Though not seen on the show much in later seasons, Ned and Jimbo qualify.
Lyra and Bon Bon are a funny case. Once crowd-filler characters who stood side by side sometimes, fanon latched onto them and they became the entire fandom's OTP, to the point that more fanfics than not have them Happily Married even if they're not the focus. Eventually the writers started playing with it, having them constantly refer to each other as 'best friends' while taking the Les YayUp to 11. As such, they're the most touchy-feely 'best friends' you ever saw, and when arguing it was played as a marital dispute. Once, in a dream world, they ended up conjoined CatDog style. Their reaction? Pure delight and hugging as best they could. Whether or not their Les Yay is canon or not is a very hot topic for debate to this day.
Fanon has more such pairings, such as Derpy Hooves and Carrot Top, for one.
Starting in "No Second Prances", Starlight Glimmer and Trixie.
Daria: While there's never even any subtext of romantic involvement (Jane's sexual questioning in Is It Fall Yet? notwithstanding), Daria and Jane otherwise fit this trope, especially the way Daria gets intensely jealous of Jane's boyfriends.
The romantics angle is joked about by the show; one of the "Daria Day" marathon host segments features them as husband and wife, and in another host segment with Daria as a nude model, Jane cracks that she can paint Daria's form "from memory".
Futurama had Fry and Bender. Bender is also extremely possessive and jealous, and gets angry/weepy when he can't live with Fry, or when Fry spends more time with his girlfriend than with Bender in the second movie.
Professor Farnsworth and Dr. Zoidberg were revealed to have this kind of friendship in "The Tip Of The Zoidberg"
The Canadian cartoon Kevin Spencer features the characters of Porn Man and Afro Man, who not only co-star in the adult films they act in, but also share a swinging bachelor pad. There's no Ho Yay between them, though, since they get more than enough action both in their day jobs and at the wild parties they host in their free time.
The Platypus Brothers in Taz-Mania. To a lesser extent, Taz and Digeri Dingo since they've known each other since birth and Taz always goes along with Digeri's schemes. Why? "Taz like Dingo!"
Ami and Yumi in Hi Hi Puffy AmiYumi are like this. They live in the same dwelling...but it's a tour bus, which they travel the world in, along with their manager Kaz. Though there are times at which they appear to be a little too close not to be doing each other, they have both shown strong interest in men and fought over a male nerd, labeling them as bona fide Heterosexual Life Partners. (No Bisexuals?)
After deciding they won't fight over boys anymore they hug under a rainbow. Make of that what you will.
Tootand Puddle, two animated pigs starring in a program by the same name, based on a series of picture books, by the same name. Live together in a small home in the burg of Woodcock Pocket/Pocket Hollow and often travel together, though Toot often travels by himself.
Badger and Mole of The Animals of Farthing Wood are inseparable and they often worry about each other when one of them goes missing with Mole being the most emotional about it often bursting into tears, in fact after Mole dies Badger just can't accept the fact he mistakes Mole's son Mossy for him as they look alike and he goes along with it because he was told it would break his heart he remains his companion until Badger passes away of old age.
It was different in the books however. Badger never died, but Mossy did. Badger found the body and as such, it's pretty clear that he can't go into denial a second time.
Virgil and Richie from Static Shock. Helped along with the fact that it's been admitted that Richie is gay by the animators and in the original comic Rick, who Richie is based on, is gay and there is even an arc where Virgil deals with his feelings on the matter.
The Venture Bros. has Henchmen 21 and 24. 21 even lampshades this in a third-season episode, when The Monarch doesn't know who 24 is.
"You know whenever you're talking to me, there's another guy with me? That's 24!"
The "Jet Boy, Jet Girl" conversation.
The Venture Brothers is nothing but Heterosexual Life Partners. Even if you don't count the aforementioned, plus the eponymous characters, you have Brock and Rusty, Pete and Billy, Tim-Tom and Kevin, Watch and Ward, Shore Leave and Mile High. And the creators of the show, who most of the characters are based on in some sense.
Mac and Tosh otherwise known as the Goofy Gophers from Looney Tunes they are super polite to each other and agree with what the other says, many people have mistaken them for gay but in several cartoons they have fallen in love with female gopher disguises.
To a lesser extent, Buford and Baljeet, whose bully/nerd relationship is portrayed more like a weird kind of friendship.
It's worth noting that Buford and Baljeet's song "Frenemies", while more about their status as Vitriolic Best Buds, includes such lines as "He's like my least favorite brother" and "We're Frenemies 'till the end."
Candace and Stacy also count for this.
Skwisgaar Skwigelf and Toki Wartooth from Metalocalypse are a fairly good example of this trope. While they constantly bicker over Toki's role in the band and Skwisgaar is just generally a Jerkass to him in almost all of their interactions, they often choose to hang out with each other exclusively and once in a blue moon they will come to the other's defense (Skwisgaar in "Dethrace", for example). They've also waxed philosophical together about subjects such as family and women (well as philosophical as you can get withthisshow). Considering that Toki has stolen Skwisgaar's clothes to emulate him in a Dethklok tribute band, offered him a blowjob in exchange for not getting kicked out of the band, and dated a girl that looked exactly like a female version of Skwisgaar, some fans would argue that Toki is or was actually nursing something of a Tsundere-esque crush on him.
It's worth noting that when Toki hangs out with another guitarist in Dethlessons, Skwisgaar's confrontation almost sounds like someone finding their spouse with another partner. And Toki's line "I've always hated you, Skwisgaar" in the first season finale is met with an almost affectionate sounding, "I knows, Toki. I knows." The previous line, in which Skwisgaar's post-mortem plans include hanging out with Toki in Valhalla. Often times they hate each other, but they're also incredibly dependent on each other.
Every possible pair in the band can be taken this way, allowing for a certain amount of belligerence and the fact that all five of them are complete idiots, except for Pickles, whose intelligence is completely sublimated by his being constantly balls-to-the-wall high, drunk, or some combination of the two.
Hank, Bill, Dale, and Boomhauer have these moments between each other. One episode (with an Overly Long Title) even dealt with a feud between Dale and Bill over a littered beer can being seen as a couple having marital problems.
Poison Ivy and Harley Quinn in Batman TAS, one of the few villain team ups that is based on friendship, rather than mutual gain. Though the Word of Gay probably strikes out the "heterosexual" part.
In Invader Zim, Red and Purple. An unfinished episode reveals they were hanging around each other even before being appointed co-rulers of the Irken Empire. One could also argue Zim and Dib, in a weird, twisted sort of way.
Chet and Lorenzo, the step brothers, initially bickered with each other nonstop but become this trope when they reach Australia.
Rock and Spud.
Valentina "MacArthur" Escobar and Sanders.
Russel Hobbes of Gorillaz actually described his best friend Del as his soulmate - he was, since Del's ghost lived in Russel's brain for several years. Russel is the only one of the three living male band members who doesn't have numerous illegitimate offspring, and we've never heard about any women in his life, so, um...
Fanboy and Chum Chum are two best friends who live together in a water tower with no parents whatsoever. Taken to the extent that the very stability of the fabric of the universe depends on them being together.
Buck Tudrussell and Larry 3000 from Time Squad qualify. Even though they go at each others throats a lot due to Tudrussell's laziness, aggression, and inconsiderate behavior and Larry's obsessive, overdramatic, and effeminate behavior that constantly shifts around Ambiguously Gay and Camp Gay, which Tudrussell often berates and makes fun of Larry for, they still remain good friends. The "Heterosexual" part of it does sometimes hang by loose threads in some episodes though.
The show's version of Lewis and Clark also qualify as even though the show made them act as if they were a couple, their friendship was actually platonic in real life.
Robin and Kid Flash in Young Justice. They have arguably the closest friendship on the show— while the four original sidekicks were all good friends and they quickly accepted the new guys, these two were already best friends. While Batman has told Dick not to reveal his secret identity to his teammates, he told Wally anyway. In a show with "secrets and lies" as a central theme, these two stand out because even when Dick tries to keep secrets from Wally, Wally knows him too well not to figure it out.
Mordecai and Rigby from Regular Show. "Bros" in the standard definition, as they act like two college roomies.
Finn and Jake from Adventure Time, though raised as brothers, and referring to each other as 'brother', are this to a T.
Princess Bubblegum and Marcellene. Even though Word of God states that they used to date, their relationship somehow morphs into just being close friends but Princess Bubblegum seems to want to date Marcellene again.
Gumball and Darwin from The Amazing World of Gumball. They would spend nearly almost all their time together and have a very close bond, though justified since they're both family and the two often consider themselves "brothers".
Hack and Slash from ReBoot exemplify this trope. They are literally never seen on screen without one another. They even get blown up by Hex together. (Then Phong put them back together and reprogrammed them, hence their Heel–Face Turn.)
Also Dot and Mouse, as well as Enzo and Frisket. Bob and Matrix also become this when they meet up again in season 3.
Thomas the Tank Engine: Thomas and Percy have become this, most especially in the later seasons. Gordon and James can also count, especially in the earlier seasons.
Mike Chilton and Chuck from Motorcity. They call each other "Mikey" and "Chuckles" at time and Mike always has his back for Chuck, as the latter is the Cowardly Lion / Non-Action Guy. Chuck does manage to go out of his way for Mike in "Fearless" though.
Randy and Howard from Randy Cunningham: 9th Grade Ninja have this, having been inseparable since childhood and even being close enough to share each others underwear.
Sam and Max Freelance Police of course, but moreso than the comics, they play with that dynamic in...very...interesting ways (mostly revolving around Sam and Max's violence fetish, although with Max, violence isn't as much a fetish as a sexual orientation.
Mandrake and Lothar have this type of relationship in Defenders of the Earth. Throughout the series, they are shown to be fiercely loyal to each other and are rarely seen apart. Also, Lothar will often go out of his way to rescue Mandrake from life-threatening situations, though the roles do get reversed a couple of times. In the original "Mandrake the Magician" comic strips, the two characters had a master/servant relationship; the fact that they (plus LJ and Kshin) were living together before the Defenders were formed is almost certainly a relic of this.
Oscar and Wilde from George and Martha can qualify for this even though they are named after a British author who had a questionable orientation, have never flirted with anyone, and there was some Ho Yay going on towards them. However, the show never goes into detail on the nature of their relationship
Darel and Gee are stated to be best friends. Darel even goes as far as attempting to rescue Gee from the scorpion army for three whole episodes.
King Sergu and Yabber. Yabber stated that he and Sergu were as close as "surf and turf" and "sand and sea". The fact that Yabber is Sergu's best student helps.
Arnold and Gerald, as well as Helga and Phoebe in Hey Arnold!.
The eponymous Pickle and Peanut have this dynamic; if they're not working together at the Mjärt Mart, they're inevitably going on misadventures with each other.
Buddy Thunderstruck and his mechanic Darnell Fetzervalve. The two of them are always together, to the point where they even live and race together. Prolonged separation from Darnell is even seen to cause anxiety and depression in Buddy.