Keichii of Higurashi no Naku Koro ni's demise at the hands of Takano Miyo. A Shut Up, Kirk! moment which had an immediate and demoralising effect on the entire group, turning a genuine fight-back into a hopeless rout.
Digimon Adventure: The Chosen Children go through this after Taichi's disappearance. After failing to find him, the kids go separate ways and fail to do anything important for months on end. When Taichi finally returns to the Digital World, he has to get his friends back together to continue their mission.
Berserk: The Band of the Hawk manages to avert this when Griffith is imprisoned, since they have hopes that they'll one day rescue him and things will go back to how they were before. Once Guts returns and they rescue him, however, they lose it once Casca can no longer hide the fact that Griffith, who's tendons and tongue were cut out while in jail, will never be the man he used to be. The entire Band goes into Heroic BSOD, which of course is the moment for Griffith to start the Eclipse...
The group of fugitives in Negation went through many deaths, but Matua's death was arguably the one that really made them begin to despair, partly because of the way he died, partly because he was just a nice guy that everybody liked. Indeed, inscribed on his grave marker were the words, "he deserved better."
Hades attempts to invoke this during the DC Nation Olympics arc - twice. All it succeeds in doing is pissing off the Titans (and Arrows, and Lanterns) to the point where Athena herself has to call a halt to things.
The group of Animorphs breaks up for various reasons once or twice. And near the end of the series there's a period where they all fucking hate each other.
The loss of the Silmarils, as well as the darkening of Valinor, has this effect on the Valar in The Silmarillion. However, it doesn't have this effect on a large group of Elves, who simply decide to go on a Roaring Rampage of Revenge instead.
In J. R. R. Tolkien's Lord of the Rings, this happens to the fellowship when Gandalf falls in Moria. Even though he's not really dead, they don't know this. Aragorn manages to pull them together long enough to get them to safety.
In Sandy Mitchell's Ciaphas Cain novel Duty Calls, Cain is bewildered that anyone would go to extensive efforts to assasinate him when there were so much less expendable targets. Amberly Vail comments in a footnote that he obviously didn't consider the effect on morale of his death, which would have been horrific.
This is illustrated later in the same book when Cain is injured and an extract from Sulla's memoirs in inserted to fill in the gap. Along with the details of the battle it relates her horror on hearing that he had fallen and relief when it was reported that he just had a concussion.
In Heinlein's "Starship Troopers" when the Lieutenant is killed helping two wounded Mobile Infantry to the recall boat. The characters undergo the Heroic BSOD, but recover fairly swiftly.
In Suzanne Collins's Catching Fire, Katniss is so important to the rebellion that other tributes die to preserve her — and save Peeta, because no one can tell what she will do if he dies.
In Dan Abnett's Gaunt's Ghosts novel Only In Death, Rawn is keenly aware of the danger of what losing Gaunt means to the regiment, and flatly tells his juniors that they are to tell the men that failure on their part means Gaunt's sacrifice was in vain.
Live Action TV
In Charmed, Prue's death had this effect on her sisters. Piper reacted with a full-blown Rage Against the Heavens ("You can tell them that we buried their precious Charmed Ones when we buried our sister"), but even Phoebe was unsure how to go on without Prue.
The deaths of both Hillbilly and Ack-Ack on Peleliu cause a Heroic BSOD for Sledge's entire company in The Pacific. Although we have little time to see its full effects, the distress of his men is evident when Basilone is killed on Iwo Jima. Although he isn't dead, in The Pacific's spiritual predecessor Band of Brothers Winters's promotion out of the company and an incompetent replacement after his had-picked successor is accidentally shot and wounded by his own sentry severely impacts the morale of Easy Company during the Battle of the Bulge, particularly after Buck Compton's departure.
Merlin: The relationships between Arthur, Merlin, and the Knights are all quite strained after Gwen is exiled for betraying Arthur by kissing Lancelot.
Squad Leader works on this principle. A simulation game based on small-unit mechanics - things rarely get to consist of much more than an infantry company or a squadron of tanks - each individual platoon or infantry section has its nominated squad leader - denoting an NCO or junior officer. If this player-token is killed, lost or incapacitated, the unit it commands is effectively decapitated and can take no action other than surrender, retreat or immediate self defence. This state lasts until the unit makes contact with another squad leader who can restore the initiative. While this accurately represents real-world warfare, the game makes no allowance for the emergence of new leaders who can restore order, as sometimes happens in real warfare.
While Cloud's reaction to Aeris' death was the most noticeable, in Final Fantasy VII the entire team suffers from grief after the event, though they display an astonishing amount of faith in Cloud despite Sephiroth's apparent ability to inflict Mind Control on him when present.
In Rome Total War, some units carried a standard which if lost had a morale impact across the entire army. Also, across the entire series, if you lose a general in battle, your army will suffer a morale penalty. Lose the entire ruling family and your faction breaks up, We Cannot Go On Without You style.
The tabletop version of Warhammer, where the battle standard often has various effects on morale. The mechanics have changed over the years, but in some incarnations killing a standard bearer could rout an army.
In Warhammer 40,000, killing the Tau armies Ethreal has this effect. Either it breaks their morale, sending them fleeing, or causes them to go on a Roaring Rampage of Revenge, gunning down any enemies on their patch.
Killing the highest ranking guard in a group you are fighting in Assassin's Creed I and its sequel will send the rest fleeing potentially. Also, from a storyline perspective, Giovanni's death in the second game has this effect on Ezios family. Ezio manages to pull them together, but has to be pulled round to the idea of fighting back.
In Halo, killing the elites or brutes that are leading a group of grunts will temporarily throw them into panicked disarray. It can happen from time to time with low-ranking jackals as well in the first game, but they're usually disciplined enough to stand and fight.
"Leader dead! Run away!"
In Dynasty Warriors and Samurai Warriors, morale plays an effect on how well your AI-controlled troops do, so you can gain it by fulfilling mission objectives or killing enemy generals and lose it via failure / death on your side.
Persona 2: Innocent Sin: everything goes to hell after Maya's death, leading right into Eternal Punishment.
In Persona 3's story, Ikutski's betrayal and the death of Mitsuru's father has this effect on SEES. Happens again in grand fashion in The Answer; when the Player Character dies following the events of The Journey, the team begins to drift apart almost immediately, and the sense of regret and despondency is practically tangible. At the beginning of the game when the cast is getting together to hand in their evokers, Akihiko and Yukari don't even bother showing up.
Unfortunately that fact that s/he's working for Cerberus means that some former squad members feel that the team spirit is completely gone.
Widespread in Mass Effect 3, between the horrific casualties caused by the Reaper invasion and the seemingly invincible nature of the attackers. One of the most common sidequests is recovering an artifact or emblem of [group X] to restore their will to fight.
This happens at the end of Wild ARMs 2, after the team is forced to kill their leader Irving, who sacrificed his sister to seal the Kuiper Belt inside himself. They saved their entire universe from annihilation, but can't bring themselves to call it a "win", and walk out in a slump. Unfortunately for them, the protagonist also has a demon sealed inside of him, and it feeds on negative emotions. On the other hand, delivering a Combined Energy Attack with a "World of Cardboard" Speech is very cathartic.
Occurs towards the end of Blaze Union following Velleman's betrayal and death and Siskier's suicide. The fact that this comes hand-in-hand with The Reveal concerning Gulcasa's true identity doesn't help. While Gulcasa eventually starts to pick himself back up (with a little help from Nessiah) and most of the team rallies around him as the new Heart, it's too late for Jenon and Medoute, who betray him, which causes the party to schism even further as they and a few other members leave for good.
In 9th Elsewhere, Carmen and Eiji experience this because of the accidental destruction of the key that unlocks Carmen's mind.
In The Order of the Stick, Roy's death ultimately has this effect on the party. Their physical separation is problematic enough, but it's the loss of their guiding sense of purpose and the mediator responsible for keeping their individual neuroses in check that causes the group to fray so badly and fail to accomplish anything significant for months on end.
Justice League Unlimited -in an alternate universe, the death of the Flash results in the League becoming obsessive, world controlling Knights Templars. It's implied that the same thing would happen in the regular universe, if Luthor were allowed to come to power as president.
Avatar: The Last Airbender -this briefly happens to the Gaang when they become trapped in a desert after Appa is stolen. Aang is upset and depressed, Toph is stumbling around with no sense of direction, and Sokka and Momo are tripping on Cactus Juice. Katara on the other hand, refuses to just give up and die, and forces them all to work together to get out of the desert.
This is an efficient method of demoralizing enemy armies. Taking off the head, or offing the enemy's main motivator can do wonders to crush morale, and by extension, the enemy's will to fight. It doesn't always work and sometimes it can backfire. The death of an important figure only martyrs them in the eyes of their group and inspires them even more.
Ancient Romans had standard bearers that would carry a golden eagle as well as the unit's standard. As long as this eagle was in the hands of a Roman soldier, they would continue to fight and protect the standard bearer. If it was lost, the entire battle was considered a lost cause as well. During an invasion of Britain, soldiers were reluctant to get off the boat due to not being able to get close enough to shore thanks to enemy attacks and projectiles. The standard bearer jumped off the boat and started running into battle. He was quickly joined.
This is what battles of Ancient Greece consisted of for many years: Hoplites were deep formations of heavily-armoured men with spears and large shields, making them nearly invincible head-on. Thus, the only way to fight them back head-on was another hoplite formation. Being heavily-armoured, the formations would more smash into each other rather than kill one another - the first side to crack under the pressure would break ranks, and then flee due to having no hope of fighting the enemy formation as individuals. This eventually changed when skirmisher tactics shot at them from afar while never lettingthe slow-moving formation get close enough to hit back. Even with their extensive protection, hoplites were not completely invulnerable and would be gradually worn down.