On the subject of reality game shows, this trope does have its place in some reality game shows like Survivor or Big Brother. In both games, there're one or two people who make friends and manage to make it further. Especially given these two games have people who proudly declare I'm Not Here to Make Friends. There's almost always one person who's evicted simply because they're at the bottom of the totem pole.
In Big Brother, if the other houseguests don't like you for whatever reason, you can expect to face the public vote. This often leads to an Unpopular Popular Character, adored by the audience but disliked by their fellow players.
Several seasons of the American Survivor show that this really can be an underestimated boon. In this game, you have to convince 7-9 players you most likely evicted to vote for you to win. If you wantonly bullied your way through the game and left a trail of angry and insulting jurors, you'll probably finish third or second, while someone who got in friendly with them will be seen as the lesser evil. This is even lampshaded by Jaison in Samoa, which is perhaps the most clear-cut example of showing this trope in action. In Samoa, one player called Russell Hantz carried his alliance through the game but was an Arrogant Kung-Fu Guy. He clearly knew the game, yet apparently didn't know that the players he sent to the jury had to like him, or at least respect him. He sociopathically pushed his way through the game, and ended by bragging to the jury about how awesome he was, and was surprised when their response was, "NO!", and their votes almost all went for the girl who went around making friends with people.
One of the central themes in Super Sentai, along with love, courage, justice, and passion.
Believe it or not, on 24, this is what ultimately turns Jack Bauer back from the dark side in the final episode and prevents him from assassinating Russian president, Yuri Suvarov. When Chloe O'Brian comes for him to try to talk him down, he asks her why she came and she replies that she had to, she's his friend.
Why The Amazing Race uses teams of two, and what differentiates the show from most other competitive Reality Shows.
Angel, like Buffy, tends to play it pretty straight (although it's generally more subdued), but lightly parodied it at least once:
Angel: You may have the attitude, and you may have the power. But there's one thing you don't have and never will: friends. Four of 'em, standin' behind you with big, heavy things.
The A-Team. So much so that in the beginning of Season 5, when Hannibal, Face, and B.A. are finally captured and put on trial all three of them choose to plead guilty for the infamous crime they didn't commit because the only way their lawyer can prove them innocent is by pinning the crime on Murdock. The team realizes that if that happens Murdock will be sentenced to death. All three of them stand up and plead guilty, knowing that they will face the firing squad. They were willing to die to protect Murdock.
The basic premise of Black Hole High seems to be that, at least within the Applied Phlebotinum field of the school, character flaws trump physics. In the second episode, it makes perfect logical sense that realizing that your friends care for you can cure invisibility.
It is specifically stated, both within the show and in interviews with writers, that the reason Buffy has lasted so long as a Slayer compared to her predecessors is that she has friends — the so-called "Scooby Gang" — who look out for her. This is why Faith fails; she's unable to trust people and form lasting friendships.
Spike: A slayer with family and friends. That sure as hell wasn't in the brochure.
Played for darker twists when it's revealed that many Slayers end up dead, not because they make physical mistakes which lose battles, but because constantly fighting demons cuts away a Slayer's ties to the world until everything she fights to protect has either died or abandoned her. With nothing they appreciate in the normal world, these Slayers become Death Seekers, and Buffy is forced to fight against her own suicidal feelings through seasons 5 and 6.
In "Primeval", the Scoobies use a spell that combines all their powers into Buffy's body - becoming, in other words, the Power of Friendship given corporeal form. They proceed to demonstrate this power by curbstomping the previously unstoppable Adam.
One of the themes in Burn Notice. Michael's a bad-ass spy who can handle anything...but even he needs the help of his friends and family to save the day. Moreover, Michael has acknowledged that he is Not So Different from many of the villains his team have dealt with over the course of the series—particularly Larry (yes, Dead Larry), and in the episode "Enemies Closer" he admits that what keeps him from crossing the Moral Event Horizon is his connection to his friends. Or maybe he was only talking to Fi.
The "Power of Three" in Charmed relied on the Power of Friendship to work. At one point the sisters intentionally used their powers on each other in a heated argument, which immediately caused the loss of their powers.
Chuck Bartowski has lost his powers and nothing seems to work to restore them. And to make matters worse the bad guys capture him and his best friend (who has no idea of what he really does) and are about to execute them, with no help in sight. Chuck regains his powers.....with a simple buddy talk with Morgan.
Near the end of Season 3, the Big Bad Shaw has effectively destroyed Team Bartowski, by capturing Chuck, Sarah, Casey and Beckman. Little does he know that by now there's a second brigade to Team Bartowski - Ellie, Devon and Morgan. This second string's counterespionage credentials are practically nil — but they'll do anything to rescue Chuck, Sarah and Casey.
Throughout the series, any character who stubbornly holds to the belief that a proper spy should have no personal attachments is either shown to be at the very least wrong (Sarah& Casey, in early episodes), unlikeable (Corrina), or vulnerable to being turned (Shaw).
"The War Machines": The mind-controlled Polly clearly sees Ben escaping, and says nothing. When someone asks after him, she explains, but when he asks her why, she does not know, and after a moment, starts to remember that he had been her friend.
In the series 3finale, Martha escapes the Master's takeover of Earth and spends one year traveling the world telling everyone about the Doctor and how they're supposed to say (and believe!) "Doctor" over and over during an onconming countdown. When said time arrives, everyone in the world doing this (even the Master's human followers and his ownfreaking wife) gives the Doctor the strength he needs to overpower the Master and undo all his evil.
All of the Doctor's previous companions have shown that they're quite willing to die (in some cases, repeatedly) to protect him. "Journey's End" has Davros that the Doctor basically turns everyone who loves him into living weapons for his cause.
Rory makes a point of it too, in a somewhat different fashion, in "The Vampires of Venice" by pointing out that part of the reason the Doctor's so dangerous is because his overconfident behaviour and impulsive nature encourages others to risk their lives just to impress him. When Rory himself ends up doing the exact same thing later in the episode, in light of the previous guilt-tripping the Doctor is less-than-impressed.
In the first half of the Series 8 finale, "Dark Water", Clara, distraught over the death of her lover, Danny Pink, tries to force the Doctor to change the events that caused his death, despite the Doctor warning her of the consequences. It turns out the Doctor anticipated her grief-stricken behavior, and took precautions, so what Clara thought was a life-or-death situation was actually a Secret Test of Character, and one she failed. Then the Doctor tells her that while it won't be the way she suggested, he will help her.
This also works in Firefly. It's what Mal tries to beat into Jayne's head throughout the show, especially in "Ariel," and it's how the crew gets the better of Saffron twice.
Saffron: Everybody plays each other. That's all anybody ever does. We play parts. Mal: You got all kinds a' learnin' and you made me look the fool without trying, yet here I am with a gun to your head. That's 'cause I got people with me, people who trust each other, who do for each other and ain't always looking for the advantage.
Invoked in "Duet", the musical episode of The Flash (2014) with the song "Super Friend", where the titular character and Supergirl sing about how, despite being deprived of their respective superpowers, they still have one: their friendship.
Friends obviously. Its pretty clear none of the characters would get through any of their problems, without the rest of the gang to support them. This was established from the minute the theme song played:
I'll be there for you... When the rain starts to pour I'll be there for you... Like I've been there before I'll be there for you... 'Cause you're there for me too
On Good Girls Revolt all the girls contribute money to help Angie pay for her abortion so she can have a proper procedure and doesn't have to resort to drinking tansy tea.
Parodied in an episode of The Good Life: "You know, Tom and Barbara are the only real friends we've got. Pity they don't have any money or power."
Even though they're often at each other's throats for one reason or another, the "non-judging Breakfast Club" of Gossip Girl always band together when one of them is in trouble. As Gossip Girl herself puts it, "With friends like these, who needs armies?"
Heroes also features a lot of this, but taken to almost anvilicious (but still enjoyable) levels concerning Hiro and Ando.
This seems to be the main reason Sibuna keep winning in House of Anubis. Fabian makes a speech about it in season 2, even, claiming that while the teachers have more of the advantages, they have the team, and they'd win because they wouldn't let each other fail.
In How I Met Your Mother, Future!Ted is pretty clear to his kids that life will occasionally (or even frequently) suck really badly, but if you have friends to accompany you on your journey through it, it'll never be completely terrible.
He also notes that the pull of friendship is more powerful than any number of problems, complications, and conflicts that might get in its way: "Friendship is an involuntary reflex; it just happens."
Kamen Rider Fourze: The show is perhaps more focused on this trope than any of the other Kamen Rider shows put together, as it stars a hero who wishes to make friends with nearly everyone, and lives up to the promise by creating the Kamen Rider Club, with contains him and six other True Companions.
All of Gentaro's States' form are only fully achieved when he reaffirmed/gain friendshipnote Elec for JK, Fire with Tomoko, Magnet with Kengo, Cosmic with the entire Rider club (+ Ryusei), Rocket from Nadeshiko.
Leverage features this heavily as the team is made up of individualistic thieves who had always worked alone. One they begin working together, they realize how much more effective they were than before.
In the Red Dwarf episode "The Last Day" it's the Power of Friendship that encourages Kryten to stand against his built-in obsolescence. Although when he starts talking about "the human value you call ... friendship", Lister replies "Don't give me the Star Trek crap, it's too early in the morning."
In one episode of Space: Above and Beyond the Chigs create a weapon that is literally powered by fear (it takes normal fears that the victim has and cranks them up to the level of crippling phobia). The Wildcards stumble upon this weapon and are only able to escape and survive due to their trust in each other being stronger than their feras.
Star Trek features a lot of this; especially in The Original Series and in The Next Generation. Many episodes revolve around one of the crew being kidnapped, threatened, or otherwise in danger, and having the rest of the crew band together to save them.
Parodied in the comedy show Stella, in which the three main characters use the power of friendship to create an invisible forcefield to trap a rival group of evil paperboys that have been bullying them throughout the episode. They then threaten to use the power of friendship to crush the bullies to death if they don't cut it out. Stella's Aesop is ALWAYS the power of friendship. ALWAYS.
Ultraman Mebius: The writers took this to heart. This features Mirai making friends with people on spot, trying to teach the meaning of friendship to others, and even being REVIVED FROM THE DEAD and gaining new powers from friendship.
In the second episode of Young Hercules, Ares decides that Hercules's weakest point is his "pathetic mortal feelings", and sends Strife to attack Hercules through his best friend, Iolaus. In the end, it is Iolaus shouting Herc's name during Hercules and Strife's final showdown that distracts Strife long enough for Hercules to win the fight.