Lampshaded in the South Park episode "The Biggest Douche in the Universe," when Chef tells Stan and Kyle that Cartman is their friend whether they like him or not. This trope becomes more apparent in later seasons, once their Weirdness Magnet status has begun to wear old; the boys fall victim to All of the Other Reindeer more often, making it evident that, while their classmates may tolerate them, they don't really have any friends outside of one another. As much as they would hate to admit it, they're a textbook example of this trope.
Teen Titans gives us... well, the Teen Titans. Various characters within the show have referred to the Titans as a family. Their devotion to the team and each other has been proved countless times throughout the series.
Raven: (to her father) The Titans are my family. This is my home.
Toph acts like her real self in a way she probably never did with her biological family.
Azula, Mai, and Ty Lee are a unique subversion of True Companions. The trio have been close friends since finishing school. As time goes on, it's made apparent that Ty Lee and Mai obey Azula because they are afraid of her and see disobeying her as a hopeless and deadly cause.
This is largely the whole point of Foster's Home for Imaginary Friends, with the "Foster's Five" considering each other to be family. Pretty justified, as four of them are imaginary friends, who can't technically have blood relatives, and one is the imaginary friend of the only human, who was created by said human and owes his existence to him.
Metalocalypse: Nathan flat out confirms in FatherKlok that Dethklok is his messed up dysfunctional family.
The members of Dethklok all see each other as family, though only Toki ever says it out loud. While it's been stated that they have agreed never to interfere with each others' personal business, let alone take active joy in the suffering of each other (such as the effect that Pickles' brother's blatant manipulation of his wealthy sibling and family has on him), they do care for each other.
Considering how listless and hurt that Dethklok was by Charles' angry outbursts and unintentional neglect in Doublebookedklok (and how they could be motivated to snap out of it just by him apologizing), it's pretty much confirmed that it's not just Nathan who considers Charles an extension of the crew now.
After season 4, Nathan and Pickles have gone through a complete stage of a falling out friendship and patching it back up, with Nathan being the one to apologize. He refers to his actions as "alienating his friends" and pleads to have Dethklok back. Even Murderface at one point says that the five of them need to stick together after everything they went through in the penultimate episode.
The whole plot of The Doomstar Requiem: A Klok Opera revolves around Nathan, Skwisgaar, Murderface and Pickles admitting that Toki is not just their bandmate, but their brother, in order to rescue him and Abigail from Magnus and the Metal Masked Assassin.
Metal Masked Assassin: You took my brother from me.
Nathan: Well, we'd rather burn in hell than let you take ours.
The Freedom Fighters of the Sonic the Hedgehog cartoon are clearly a tightly-knit group of friends, all of whom have lost their actual families and so turn to each other for that kind of support; Tails even considers Princess Sally his "Aunt", and she treats him very much like her own son at times. Likewise, Sonic and Tails have a very brotherly relationship.
Chip 'n Dale Rescue Rangers: The Rescue Rangers, so much so that several episodes (including the pilot) feature one of the members leaving the group, to later return only because it's where they belong.
In Phineas and Ferb, the title characters, Baljeet, Buford, Perry, and Isabella are true companions, though Isabella has romantic feelings for Phineas. The Fireside Girls can also be considered an example. (Proof of Perry's status as a true companion: in one episode, Doofenshmirtz's 'inator of the week "will destroy ANYONE who can't make up their minds." Perry flashes back to the title characters' uncharacteristic indecision at the kitchen table that morning, and proceeds to handcuff D. to a pipe before, as usually happens, the device can be ''activated.")
Zachary: The day we don't trust one another is the day the Galaxy Rangers are finished.
Mindnet also marks the first time the Rangers "pool their badges" in a Mental Fusion tactic that is used occasionally throughout the rest of the series. Zachary is very quick to fall into the Team Dad role, especially when it comes to the parent-less Niko and Shane. Fanon states that his true-companion relationship with the Rangers is what has kept him relatively sane after the loss of his wife and his rebuilding into a Hollywood Cyborg.
It could be said that the original seven of the DCAU's Justice League are true companions. They would have to be after all they've gone through together. A great example of it this is Flash's Day in the Limelight episode of Unlimited, where Flash is able to convince Batman to come to the opening of his museum with little more than a "please," and delivers a brief but touching "you don't understand" at Orion, who straight up asked how he can put up with the Flash's antics and methods.
Most of the combiner groups in The Transformers and Transformers Prime, especially the Aerialbots and Team Prime but this trope is subverted for the Combaticons. For a group of villains, the Combaticons have had scenes together that are downright touching and they work well together (particularly when all the world is against them), but they were thrown together purely by circumstance, and Swindle has no loyalty to them at all (he once literally sold the others for scrap!).
The Maximals in Beast Wars were often this, but usually not everyone on the team had membership in the inner circle. Optimus, Rattrap, Rhinox and Cheetor were the core four with other members of the team (Dinobot, Depth Charge, Airazor, Blackarachnia, Silverbolt on occasion, and Tigatron of his own accord) being treated more as outsiders and generally not trusted with the same responsibilities and inside information.
Optimus explicitly refers to his group (himself, Ratchet, Prowl, Bumblebee, Bulkhead and Sari) as a family in Transformers Animated.
Team Prime from Transformers Prime are especially close, since they are, as far as they know, the sole surviving Autobots in the universe. Established in a single word in the very first episode, when Bumblebee shows up to back up Arcee in a fight.
Jack: Friend of yours? Arcee: Family.
The Rugrats babies are pretty much always together, and it's often hard to believe that the in-universe time the series takes up would have to be less than a year or two. Even Angelica is included.
Twilight Sparkle, Spike, Pinkie Pie, Applejack, Fluttershy, Rarity, and Rainbow Dash. It's a series about The Power of Friendship, after all. They may fight sometimes, but it's crystal clear that, no matter what, there's no way they're abandoning one another.
"The Super Speedy Cider Squeezy 6000" takes this to its greatest height yet. During the competition for the farm, Applejack allows the others to help her and her family. Why? Because she now considers them her family. Cementing the mutual feeling is Twilight referring to herself, Fluttershy, Rarity, Rainbow Dash, and Pinkie Pie as "honorary Apple Family members" as a loophole to help in the competition, as well as the expressions on their faces when Applejack accepts their help by calling them her family.
In "Dragon Quest," Spike also calls the others his family after going out to meet other dragons to find out who he is, and learning An Aesop that seeing this in terms of his biological origins was missing the point.
This is taken even further in the Season 3 finale. Five members of the mane six have their memories and destinies altered thanks to a botched spell. Despite having lost their original talents, they more than happily try to perform those skills once their friends inform them that one of their number is in trouble, and doing so can help. This is simply because they still know, despite everything, who their true friends are; even if they don't think they can help, it doesn't stop them from doing whatever they can. The song that plays during this sequence of events, "A True, True Friend," is basically this trope in a nutshell. It was that same power of friendship that allowed Twilight to finish Starswirl the Bearded's unfinished spell, thus becoming a new alicorn princess. For her to become a leader, she had to bond with her friends and accept their help to become what she was being developed by Princess Celestia to be.
The members of Young Justice, as exemplified in the episode "The Usual Suspects", where Superboy, Artimis, and Miss Martian each admit to keeping major secrets from the rest of the team and are immediately forgiven.
The runaways also count. They may not always agree, but they will stand by each other.
All of the ThunderCats. The ThunderCats (2011) reboot is very dysfunctional, mostly because of Tygra and Lion-O's tense relationship and the love triangle with Cheetarah, and loyalty turns out to be a big issue for the team. They stick together when it counts, and towards the end it seems like the main cast are finally true companions.
All of the engines from Thomas the Tank Engine are considered this. Despite having their quarreling, which most of it involves teasing each other for their misfortunes and humiliating situations, at the end of the day, they will always look out for each other and are willing to help each other whenever they're in serious trouble.
Jem/Jerrica and all of the original Holograms on Jem and the Holograms are a fine example, seeing how they were all sisters (Jerrica and Kimber are biological sisters while Aja and Shana are their adopted sisters.) On the flip side, you have the original three Misfits. Some of the best pieces of evidence for this is their behavior towards one another on Island of Deception and in the song We're Off And Running.
Thundarr the Barbarian, Princess Ariel, and Ookla the Mok were completely inseparable and each was absolutely loyal to the other two. It's too bad the makers of the cartoon never told the story of how they all met each other.