Code Geass ends with an interesting literal and metaphorical variation: Lelouch passes the Zero identity to Suzaku specifically so that he can become a hero by killing Lelouch per his plan to achieve world peace, using Lelouch's own goofy pink sword to do the deed, leading to a Bittersweet Ending.
Gundam 00 has Lyle Dylandy take up his brother Neil's position as Lockon Stratos in the second season.
In Shikabane HimeWhen Keisei dies and Ouri takes his place as a contracted priest.
The Lensman anime opens with a Lensman crash landing in front of the hero, and passing his Lens along before he dies.
Strongly implied to be Meg's eventual destiny in Burst Angel, after her partner Jo's apparent death and the destruction of RAPT.
In the fifth arc of Umineko no Naku Koro ni, Beatrice is killed by Erika Furudo. As a result, Battler becomes the Endless Sorcerer. An interesting example, considering that he's taking up the role of the woman who has acted as an antagonist until now.
In Naruto, when Shikamaru's teacher Asuma dies, Shikamaru inherits his chakra-enhancing blades, with which Shikamaru kills his teacher's killer.
A villainous example is Madara passing his identity and plan on to Obito.
In Yu-Gi-Oh! 5Ds, Crow's duel disk and duel runner were originally owned by his late hero, Robert Pearson.
Heartcatch Precure plays this oddly - the Call to Adventure dream Tsubomi, Erika and Itsuki get implies Cure Moonlight died. Tsubomi even gets Moonlight's Kokoro Perfume. That's not the case - Moonlight is still alive, back in her civilian identity as Yuri and suffering from a very bitter 10-Minute Retirement.
A non-lethal example occurs in the Kirbyanime, where one fight against a particularly powerful demon beast leaves Meta Knight in a coma that can only be cured if the demon dies. Naturally, Kirby grabs his sword and heads off to fight it.
This is a mechanism built-in to the Green Lantern rings and it seems most Lanterns gain their ring immediately in the wake of their predecessor's death (Genre Savvy villains, e.g. in Justice, abused this rule by incapacitating the current GL without killing him, so that his successor isn't "activated"). Sometimes the Lanterns recruit and sometimes a dying Lantern gets to play the Take Up My Sword trope straight as Abin Sur did with Hal Jordan.
Elfquest. Played straight with the sword New Moon, forged for the wolfrider chieftain Bearclaw. When he dies, he begs his son Cutter to finish the job, and literally invokes the trope:
"Finish it for me... Tam, my chief-son...Take New Moon. Your hand is mine now...When you strike...I will strike too..."
Batman does this twice. The first time, Bruce Wayne gives the Mantle of the Bat to Jean-Paul Valley, only to take it away after he goes nuts, and temporarily gives it to Dick Grayson. When Bruce was declared dead at the end of Final Crisis, Tim Drake and Jason Todd become Batman before Dick takes up the position (and keeps it long after Wayne returns) as Batman.
Interestingly, Dick has stayed as Batman even after Bruce's return to the costume. Bruce is out and about taking his operation global with ''Batman Incorporated'' while Dick is the Batman of Gotham.
The Death of Superman led to no less than four Supermen standing up to replace or impersonate him. Three were Anti Hero Substitutes; the fourth was as much of a Cape as the original (if not more so), and was regarded as a legitimate successor to Superman even after the original returned.
The Death of Spider-Man, Ultimate Spider-Man to be specific, led to new character Miles Morales to take up the mantle. The first arc of the new Ultimate Spider-Man series gave a Perspective Flip in which it's revealed that Miles had his power long before Peter ever died. He was adamant not to become a Super hero however. After learning of Peter's death however, Miles was overcome with guilt due to his own inaction, and decided to carrying on his legacy.
And now in the mainstream universe, Peter Parker, his consciousness trapped inside Dr. Octopus' dying body, is able to convince Octavius, who is inhabiting Peter's body, to stop being a villain and not to soil the name of Spider-Man with his villainous acts. Octavius agrees, setting the stage for him to become the Superior Spider Man.
Winter War takes the view that Tousen's zanpakutou Suzumushi originally belonged to his dead friend, and that after her murder, he essentially took on her (sentient) weapon and powers as well as her goals. In the present of the fic, with Tousen dead, Suzumushi is actively trying to get someone else to "take her up" and use her powers to pursue Tousen's "justice"... although she'd really prefer to just possess someone, rather than allow a shinigami free rein with her powers. Nanao finally persuades Suzumushi to temporarily lend her her powers, until they have accomplished their common goal of killing Aizen.
At the end of Game Theory, Yuuno gives his Device to Momoko, setting things up for the sequel.
The Mask of Zorro: It isn't clear if the sword the new Zorro uses is in fact the same one as the one used by the original, but he received the mantle of Zorro all along.
Can someone tell me where this fits: In the new Star Trek movie, Nero kills Lt. George Samuel Kirk as he tries to stop him. But 25 years later his son finishes the job. But nothing as actually passed down, per se.
A more straightforward example would be Spock (and later Kirk) taking over from Pike.
If anyone finds a place for that, 300 belongs there as well—Leonidas and his 300 die (except for one survivor), but their deaths inspire the rest of Greece (led by the aforementioned survivor) to fight back and drive off the Persians.
In Highlander, Ramirez finds and trains Connor MacLeod so that somebody would have a chance of defeating the Kurgan. When the Kurgan takes the aged immortal's head, Connor takes Ramirez's sword and uses it as his own from that point on, later using it to behead the Kurgan and fulfil his mentor's wish.
From "Sharpe's Rifles" -
Captain Murray: "I want you to have my sword. Maybe if the men see you carry it—"
In Braveheart, the honor of course goes to Robert the Bruce, but Wallace's best friend gets the literal sword, and throws it, in an act of defiant symbolism, to what can be considered the climax of the entire musical store.
A Song of Ice and Fire apart from several literal heirloom swords, has various examples of quests being passed on.
After Viserys finally pushes Khal Drogo too far, Daenerys takes up the quest to lead the khalasar on a war of conquest and eventually regain the Iron Throne.
The Lord Commander of the Night's Watch grooms Jon Snow for leadership, and gives him a Valyrian steel bastard sword as a token of his esteem.
Jaime Lannister was released for a secret exchange of captives, only to find that the captives that would have been traded for him had already escaped on their own and vanished. He was unable to hunt for them himself due to his duties as Lord Commander of the Kingsguard and the loss of his sword hand and passed the quest on to Brienne of Tarth, along with a sword which had been forged from the remains of Ice.
As mentioned in the Film section, Sharpe receives his dying captains old cavalry troopers sword (bear in mind both are infantrymen and it is 35 inches long) in Sharpe's Rifles.
Sam in The Lord of the Rings becomes the Ringbearer after Frodo seemingly dies. However, they later meet again, and Sam, so to say, "gives the sword back" to Frodo.
Lan is an even better example of this, as he was given his fathers sword while still in the cradle!
What about Rand? In a really weird form of it since the person encouraging him to take up his sword is Rand's past life.
There's a version of it in Green Rider by Kristen Britain, where a fallen messenger gives a girl his magic brooch and Cool Horse so she can carry his message for him.
Not quite the same, but in The Dresden Files, Harry is given two Swords of the Cross on separate occasions to find replacements for their original wielders.
In Dan Abnett's Xenos, Voke, who may be dying, asks Eisenhorn to sponsor a protegee of his, if necessary. Besides providing for the future, this is also a gesture of respect, because of their conflicts earlier in the novel and Voke's then expressed opinions of Eisenhorn's methods. (Turns out not to be necessary.)
In Dan Abnett's Warhammer 40000 novel Brothers of the Snake, several marines in Damocles die on different occasions. On the first, Priad is told that he must take up leadership and receives the claw which the leader of the squad always carries; on the second, the survivors seek new ones to take their place.
Throughout the Redwall series, various characters have gotten messages from Martin, either written down or in dreams, telling them to take up his sword and defend Redwall Abbey.
Fear Street Cheerleaders by R. L. Stine does this halfway through the first book, with the seeming protagonist boiled to death, but her sister continuing to fight the being that killed her.
In Animorphs, an injured Elfangor gives the kids the power to morph only minutes before Visser 3 eats him. And it's made more literal since one of the kids, Tobias, is Elfangor's son, though he doesn't find that out until later. Elfangor realized it, though Tobias has his doubts.
In a villainous example, this is what Tigerstar intends for Brambleclaw, Hawkfrost, Tawnypelt for a short time, Jayfeather for a short time, Lionblaze, and Tigerheart. He succeeds with one of them. Who then dies.
In the beginning of Cyteen by C.J Cherryh, Ariane Emory dies. Before she died, she had been working on a project to clone herself, and the project is continued after she dies.
In Guardians of Ga'Hoole, Soren takes up the battle claws of Ezylryb after the old owl's death. He wears them during the final battle against Nyra's forces.
In The Amazing Adventures of Kavalier and Clay, Joe Kavalier and Sam Clay are the creators of the Golden Age hero The Escapist, whose origin embraces this trope: escape artist Max Mayflower, aka Misterioso, was shot by a sniper while in the midst of performing an elaborate escape onstage. As he was led offstage by his assistants, Max convinced his nephew Tom to finish the act wearing Max's Misterioso costume. Tom, who before had been crippled, was able to perform the rest of the show flawlessly, as becoming Misterioso somehow restored his strength and cured his legs. Later, before dying of the gunshot, Max revealed to Tom that he worked for The League of the Golden Key, an organization that worked to liberate people who have been enslaved or wrongly imprisoned. His killer was a member of an international slave ring called the Iron Chain. With Max's death, Tom took his place in the League, forging the identity of the Escapist.
Live Action TV
Leo in Power Rangers Lost Galaxy took his brother Mike's sword as he was about to fall to a pit, and became the Red Ranger. His brother had the sword for about 5 minutes, but that's besides the point...
Lost Galaxy actually has two more examples of this. Both the Magna Defender and Kendrix had Heroic Sacrifices, and their spirits came back to officially bestow their swords and powers on successors (Mike and Karone, respectively).
Robert of Huntingdon (played by Jason Connery) succeeds Michael Praed's Robin of Sherwood as 'the Hooded Man' and bearer of the magic sword Albion.
She was a heroine for the whole series, even if she was a sidekick. There is a literal 'take up my chakram' scene, though.
Gary from Early Edition gives a little girl a Swiss Army knife with her initials, the same one Lucius Snow gave to him.
Not quite so dramatic, but in The Magnificent Seven, Mary Travis runs her husband's newspaper after his murder. (Not a spoiler, as he's dead before the pilot episode.) And she is very much a crusader.
Perhaps ER may count as well, even if it's not a superhero series: when Mark (protagonist of the first eight seasons) has his last day at the hospital, his last words before leaving are "you set the tone, Carter." After he dies, Dr. Carter "inherits" Mark's stethoscope.
Wild Bill Hickok from Deadwood is introduced as though he would be a major character, acting as a sort of surrogate sheriff for the town. After his murder, Seth Bullock took on the role of the town's conscience, eventually becoming the town's actual sheriff. Similarly, after Brom Garrett's murder, his widow (who had previously shown little interest in anything other than laudanum), rose to the occasion and fought to secure her late husband's gold claim and to try and get some kind of justice against his killers.
Kind of given a part two in the second Double movie, where Sokichi appears to Shotaro "beyond the grave" as Kamen Rider Skull, giving his former apprentice the Lost Driver and enabling him to become Kamen Rider Joker.
Each of the final three episodes of Lost features an instance of this. First, a flashback episode reveals that Jacob's adoptive mother transfered her powers (most prominently immortality) and position as the Island's protector down to him shortly before she was killed. Then, Jacob briefly comes back from the grave in order to do the same for Jack Shephard. Finally, as Jack is dying, he decides to transfer the powers and responsibilities to Hurley before performing a Heroic Sacrifice. This can be assumed to be a pattern that started long before the events of the show and will continue long after the final episode.
Combined with Passing the Torch in Doctor Who's "Time Crash", which, despite the time differential (it aired two years after the revival premiered), can be seen as Classic Who passing the torch to New Who.
The Sarah Jane Adventures can also be seen as this. It is, essentially, Sarah Jane taking on the Doctor's role of defending the earth. Somewhat subverted in that the Doctor isn't actually dead. But he's not always there when the earth needs saving. And that's where Sarah Jane and her team come in.
In the Red Dwarf episode "Stoke Me a Clipper", Arnold Rimmer reluctantly becomes the next "Ace" when the previous one shows up mortally wounded.
Highlander episode 'Homeland'. After Duncan was cast out of his clan, it was attacked by a Viking named Kanwulf, and his father was killed. Duncan came back and took up his father's sword to go after the guy. Unfortunately, he didn't know the rules of immortality at the time, so he didn't behead Kanwulf and the guy survived. Duncan, however, became a legend. "He came back from the grave, took up his father's sword and slew the Viking." When Kanwulf returns in the present day to terrorize the village until his sacred ax is found, Duncan repeats the legend, taking his father's sword from the inn/tavern where it had hung and finally ending Kanwulf for good.
Primeval involves the team leader Nick Cutter for two series dying, and telling Connor Temple to finish his work. These are his last words, and Connor investigates anomalies and ends up killing Helen Cutter, Nick's killer, and continuing his research into anomalies.
Hercules passing on his bow and arrows (tipped in the blood of the Hydra) to Philoktetes.
This is repeatedly Lampshaded in The Quran, citing the possibility of Muhammad dying in battle, and what the rest of the Muslims must do in case that actually happen. History says otherwise, though.
This is the big reason why the Vampires don't go out of their way to kill Hunters in World of Darkness. Kill one, and you'd just get one or more to take their place.
In Wicked, Elphaba hands the Grimmerie off to Glinda before "melting."
In The Ring of the Nibelung the sword Notung is first placed in a tree by Wotan for his son Siegmund to find, after it shatters in Siegmund's final fight the shards are picked up and handed over to his sister Sieglind. The shards wind up in the possession of their son Siegfried, who reforges them.
Played super-straight in Final Fantasy V, and even within the game mechanic. When Krile replaces Galuf in your party following the latter's death, she gets all his old abilities and exp and suchlike.
Subverted in Tales of Monkey Island. At the end of chapter 4, Guybrush died and it looked like Elaine would be the hero of the final episode (she even gets a Crowning Moment of Awesome in chapter 4's end cinematic, as if confirming this idea). A month later, chapter 5 came out and the focus was still on Guybrush.
In Super Robot Wars Original Generation Gaiden its revealed that Fighter Roar tried to use a kamikaze attack on Dark Brain and is now without a body. He then merges with Kouta so that Kouta can become the new Fighter Roar with the first Roar being his Obi Wan.
In Ace Attorney Investigations, Kay takes up the position of Yatagarasu from her father.
Several more, Phoenix succeeds Mia who then entrusts him with the safety and happiness of her little sister and Phoenix later trains Apollo to be the kind of lawyer he was.
Also, Mia takes up what is hinted to be Deigo Armando's position as the hot-headed, never say die defence attorney as well as the case against Dahlia Hawthorne after his poisoning.
The Crucible in Mass Effect 3 is an ancient weapon against the Reapers that was never finished before its creators where wiped out. But it wasn't developed by the Protheans either. Like the humans, they found the plans in ancient ruins 50,000 years older than their own civilization and only improved and refined what they found. It's the combined effort of countless civilization which each added new improvements to the design before they were annihilated by the reaper, making the building of the Crucible a task that has been passed down for millions of years, with the current cycle of reaping that Humanity is part of being the first to actually finish it.
A variation of sorts occurs at the end of Legacy of Kain: Defiance. Instead of handing over a sword, Raziel willingly lets himself be absorbed into the Reaver, so Kain can continue to fight the good fight.
Of course, we can't forget Link taking his uncle's sword in The Legend of Zelda: A Link to the Past where he finds his uncle dying in the sewers of Hyrule Castle, is told to take his sword and save Princess Zelda.
In Mega Man Legends 2, the part needed for the blade arm weapon is called, "Zetsabre", with its description going something like, "an ancient and mysterious weapon." An alternate translation give the name as "Z-Sabre". Any guesses as to who's weapon that was?
In Chrono Trigger, Frog eventually takes up the legendary Masamune in memory of his brother-in-arms Cyrus, who was killed just as the sword was recovered.
The big Reveal of the heavily Mind ScrewedMetal Gear series turns out to be that the entire situation with Outer Haven, Metal Gear, Les Enfants Terrible, the Patriots, and FOXDIE is just the result of a small group of people fighting about how to best continue the work of The Boss.
Kingdom Hearts Birth By Sleep: Aqua takes up Eraqus' keyblade when returning to Land of Departure aster his death, and start wield it after losing her own to save Terra-Xehanort. The bequething ceremonies Aqua and Terra give to Kairi and Riku also qualify by the end have effectively passed on their roles in the story to them.
A variation in The Last Story: the sword that Quark wears on his belt is symbolic of his childhood oath with Elza for them to become knights and protect people. Later, Quark pulls a Face Heel Turn and tries to kill the party. After his defeat, he passes on this sword to Elza, acknowledging that he lost faith in their dream and that Elza never did.
In Phantasy Star IV, Alys' death forces Chaz to assume command of the team and continue the mission to stop Zio.
Dragon Quest V, Pankraz's trying to find his wife, and passes on the job to his son as he's dying, setting up one of the main objectives of the game.
Happens several times in the Modern Warfare games. In 1, Sgt. Jackson gets killed by a nuke, although that's a weaker example, since you were already playing as Soap, who the story shifts to, anyway. In 2, It happens twice- first, Allen gets shot by Makarov and you become a different US Army Ranger in the same unit for the rest of the American side of the story, and later, Roach dies when Shepard betrays Task Force 141, and you play as Soap for the final few missions 3 is the only game in the series to (mostly) lack this trope- a few characters die while you play as them, but you only play as them for one level anyway, and nobody new replaces them.
A literal case occurs in Alone In The Dark 2. A captain killed by the Big Bad claimed that he would die by the captain's sword. In the final battle, you need to get the sword (Which has been stuck in the planking of the ship's quarterdeck for centuries and is still in usable condition for some reason) to win the fight.
In ReBoot, Bob gives Enzo a copy of his Guardian Code & uniform just in case something happens to him during the Web invasion. Sure enough, Bob gets betrayed by Megabyte and exiled to the Web and it's up to Enzo to take Bob's place as guardian of Mainframe. Enzo even gets to use Bob's (broken) Glitch for a while. However Give Back My Sword occurs later when Bob returns and takes Glitch back without even asking for it.
Mind you, Glitch was still broken at the time, and Enzo had grown up as a virus-hunting warrior without using it.
They tried to do this with Matrix's backup clone, little Enzo. Fortunately for everyone, Little Enzo refused.