The hero may have a chance to redeem himself, and usually the rest of the squad is beleaguered while the hero learns his lesson and joins in with new skills and determination sorely needed, becoming the team's needed leader once again.
Alternatively, the hero and his lancer or other capable member may change positions. (Expect this one to cause trouble later.)
The hero may find himself Jumping Off the Slippery Slope as a Fallen Hero. This will also cause trouble as he's often one of the strongest characters, especially if his team abandoned him on moral grounds, and this kind of split is almost always on moral grounds as grounds of competence would simply lead to demotion.
If there were people who still agree with the current hero, there may be a case of Divided We Fall as the heroes turn on one another.
Rarely, it turns out that the companions are becoming more morally ambiguous or even outright evil while The Hero is still morally upright. The companions disagree with The Hero's dog petting, refusal to Shoot the Dog, and their general policy of Honor Before Reason. Depending on the tone of the story, the companions are either brought around, manage to corrupt the hero too, or force The Hero to find new True Companions.
Finally, on very rare occasions the hero and his team may split off entirely, the former hero eventually joining up with another heroic, neutral or evil group while the rest continue on.
Contrast Divided We Fall, where dissension arises despite the hero being in the right. Sub-trope of We ARE Struggling Together, which covers general good guy division.
The reasons for using this trope are numerous; it provides a moment of introspection for the hero and audience for the hero to really come to grips with his or her ideals and true feelings... and how far the hero has fallen away from them. And, perhaps, how that selfishness in putting the heroes own feelings above the needs of the group has led him away from cherished ideals... which the character finds he or she feels even more strongly about than the issues he or she was having before.
A version happens to Hal Jordan when he becomes Parallax- he's almost immediately abandoned by his allies (though his habit of taking people's rings and leaving them stranded in space doesn't help) and even when he returns is viewed with much suspicion by the other Lanterns, with the exception of the Earth Lanterns and Kilowog.
Happens in The Outsiders (v. 3) after Nightwing's actions lead to Thunder's being injured. He's demoted, and Jade becomes team leader.
Happens briefly in Captain Blood, when Peter wants to take his crew to Port Royale where the vengeful governor and the entire English fleet is waiting to string them up. He manages to talk them round.
In The Simpsons Movie, the rest of the family want to go and help Springfield, which is in a certain level of trouble to say the least. Homer refuses (the family were out of town at the time for very good reasons.) and storms out in a huff. When he returns, the family have gone without him, leaving a Tearjerker of a message behind them.
Angel starts to lose sight of the whole redemption thing in the second season (not helped by Darla screwing with his head) and becomes increasingly morally ambiguous. When Team Angel confronts him about this, he fires them. They carry on in his absence, and he eventually comes to a realisation about what he's been doing and comes back, offering to work for them instead of them working for him. He does end up in charge again, but it takes a while.
Angel also subverts this trope in its last season. Angel starts to distance himself from the team, as well as acting more and more like he has given up on hero business and is now playing the game for his own gain only. It ends with the team confronting him in person, and just as they're about to revolt, he reveals that he's been faking it to gain the trust of the Circle of the Black Thorn.
Something similar happens toward the end of Buffy season seven. Buffy has been steadily losing all sense of perspective through the season, and eventually the potential-army confronts her about it. They're initially just trying to demote her, but when she makes it clear she won't work for them and is unwilling to run things by democracy, Dawn tells her to get out of the house.
In this case, the potentials and their new leader (Faith of all people) immediately screw up even worse than they had accused Buffy of doing, while Buffy goes off and actually accomplishes some victories on her own (including, recovering a magical weapon that ends up being the MacGuffin they need to win in the finale, and killing the Dragon). Buffy ends up back in charge, accepting that she had been overly critical and needed to accept input from other people, while the potentials realize just what a burden she had been carrying and cut her some slack.
Dragon Age: Origins has three possible occurances of this, two of which happen at the same point. These occur if you choose to defile the Urn of Sacred Ashes so the crazy man lets you into his super special club. If you have Leliana and/or Wynne with you at the time, they will openly attack you. The third happens if you haven't gotten Sten's approval high enough and you get far enough into the story. At that point he will question your leadership and if you can't persuade him, he will also attack you. Although that is somewhat less of an example than the first.
In the Avatar: The Last Airbender episode Bato of the Water Tribe, Aang hides a letter meant for the eponymous Bato because it contains the location of Katara and Sokka's father and he's afraid they'll leave him. While they had, unknown to Aang, refused Bato's offer to visit Dad, when Aang guiltily confesses they change their minds out of disgust briefly. Then they decide helping Aang was more important after all, and nothing more ever comes of it.
Also played with in the second season, when Appa is kidnapped, Aang has a Heroic BSOD and lashes out at everyone. He (emotionally) abandons them rather than the other way around, forcing Katara to take charge.
The cartoon Noahs Island has an episode where the entire island rebels against Noah for an episode. The following episode opens with them holding a vote and making him captain of the island (said island is a drifting section of another island) again.
In South Park, Cartman forms the "Coon & Friends" supergroup for his "superhero" alter-ego The Coon, along with the rest of the group coming up with their own more or less imaginative superhero personas. Cartman's usual behavior persuing a superhero that won't join his group and trying to blackmail him into joining eventually makes the rest of the group kick him out. Although, they still keep the group name because "it pisses him off so much" and continue meeting in his mom's basement. In retaliation, Cartman ends up joining with Cthulhu himself in his selfish quest at vengeance, murdering thousands in the process, all while continuing to portray himself as the hero in the Art Shift comic book narrations.