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While he did initially try to Refuse The Call, Shinji from Neon Genesis Evangelion mostly falls into this category. While he hates being a pilot and the constant stress of battle he continues to take his Evangelion into battle, and both of his efforts to stop being a pilot wind up being Ten Minute Retirements.
Sosuke Sagara of Full Metal Panic! is an odd example. He doesn't mind going into battle and fighting dastardly foes in a Humongous Mecha, really. After all, it's his job, and 'bout the only thing he's good at, having grown up a Child Soldier. However, he DOES mind being assigned to the ONLY robot in the unit which is powered by Hot Bloodedness. He frequently declares that a system so uncertain that you can only use it when your 'emotions peak' is way too unreliable to be a decent weapon, but is rather more like magic - and he's a SOLDIER, not a WIZARD! And yet, he's the only one who can use the system at ALL, so even though he'd much rather just use a bog-standard Real Robot, every time a Lambda Drive-equipped enemy shows up, he's got no choice but to climb into his Super Robot and take them on, grumbling all the way.
A side note. The reason he's the only one who can use the Arbelest is because he was the first one to use it, and since then the mech's quirky AI (named "Al") refuses to work with anyone else. Al is also wired into the device that allows the mech to twist the laws of physics, itself black box tech that no one in Mithril knows how to replicate.
In The World God Only Knows, Keima Katsuragi basically just wants to be left alone with his games, but he already signed the contract that would make his head explode should he fail to accomplish his goal. (He thought that it was a contract for a new game). So he sucked up at his job and a made good success of it. It also helps that he grows to care for the girls which contain the Weiss, because the Weiss will severely affect the girls in some way and will be reborn as the girl's first child.
Kyoko Koizumi in 20th Century Boys. She ends up involved in the whole "friend" conspiracy completely by accident, and repeatedly attempts (and fails) to go back to her normal life. Eventually she just gives in and rolls with it.
Rin Natsuki of Yes! Precure 5 thought Nozomi was nuts when she was chosen to be the next Pretty Cure, telling her "Thanks, but no thanks." When one of Nightmare's men arrive, Rin panics and tries to find Nozomi and tell her to stop being a Cure. When she refuses and gets in over her head, Rin's resigned to save her best friend, despite how scared she is, and become Cure Rouge.
Usagi Tsukino goes through this during the first half of the Filler Arc storyline in Sailor Moon R. After being resurrected following the fight with Queen Beryl, she's content as a normal school girl until the storyline's Big Bads show up, forcing Luna to restore her memories and powers. Despite this, she's completely hesitant on being Sailor Moon, causing her powers to futz up before blinking out completely. It isn't until she encounters Queen Serenity once more that she's Resigned to the Call.
In Saiyuki the fact that Sanzo is actually doing what the gods want him to in going on this quest, and even goes along with who they insist he bring along with limited grumbling seems severely out of character... until you get some backstory and realize his duty as a Sanzo priest was all that kept him from falling completely apart at a certain point in his life, and this is the best lead he's had in 10 years of searching for his master's lost sutra. Then it makes more sense that he would be resigned to the call.
For Matsuda from Front Mission, his goal was to find and bring back Inuzuka from Huffman for his War Is Hell photography. He didn't wanted to become a wartime correspondant until Reona suffered a Retirony moment and he realize at that point that he had to help continue the press.
First, there's Nanoha who took the task of being a Magical Girl simply to help Yuuno recover the Jewel seeds that were scattered in the city, treating it like a secondary objective to studying or helping in their family business. It was her first slip up with a jewel seed that she decided to take the search more seriously, and an encounter with mage more experienced than she is who is also looking for said seeds made her realize the gravity of her quest. She then realized that she would need to improve herself in order to complete her quest, as well as to save the other mage from herself (as she saw what lengths her rival would go to to obtain the seeds) and became fully devoted to magic training.
The second season has Hayate, who upon learning that she is The Chosen One, responded with what could be summed as "Sure, why not?" She was pretty content with her life, despite being a crippled girl who lives alone, and wished noting more from the Book of Darkness, only expressing happiness for it has provided her with people she can call family. After the Book of Darkness incident, she realized that she has been given an opportunity to help people in a greater way, by joining the military and keeping the universe safe from similar incidents that happened around her and as the current master of the book, feels she should share the responsibility with her guardians.
Miho Nishizumi, from Girls und Panzer goes through this several times. She transfers to a new school to avoid having to take Sensha-do, but gets drafted into the sport when the Student Council demands she participate, albeit ultimately deciding to go along with it when seeing her friends, who had originally wanted to do tankery, switch their electives to stay with her and defend her decision not to do tankery. When she and her friends form tank crew, she first refuses taking the commander position, but is talked into it by the rest of the team after the first practice. Later she gets "volunteered" to take command of the whole school's Tankery team by the Student Council president.
The Wizard of Oz gives us Dorothy and Toto. They did want to see if there was a more interesting life than their mundane home in Kansas, but they never really wanted to end up in Oz. See if The Call cared. And other than the whole being trapped indoors during a tornado thing, they sure didn't seem to have much in the way of a warning. Still, once in Oz, what were they to do?
The main character of Cellular is this. He actively acknowledges how far in over his head he is, and he does attempt to get police help in the beginning, but acknowledges that if nobody better fit to handle the situation will step up, then he has no choice but to do so himself.
Accidental Hero: Dustin Hoffman's character is a misanthropic, cynical petty crook, constantly declaring that everyone is out for themselves and no one else. Then a plane crashes right in front of his car, and a boy begs him to save his father; he looks around for a fireman, or anyone else, but there's no one else to turn to, so he goes into the burning wreck and rescues each person he comes across in turn - grumbling the whole time about his brand-new shoes. At the end of the film, with his son at the zoo, someone falls into the bear enclosure; he yells, "call the zookeeper!" a few times before reluctantly heading off to the rescue, grumbling, "watch my shoes."
Chandler Jarrell in The Golden Child is a specialist in finding missing children, but also a profound skeptic. When he is told that the titular Golden Child has been kidnapped, he's willing to consider it as just another job, and gets very annoyed when people keep bringing up supernatural stuff like that he's the Chosen One, or that the child is to be sacrificed to The Legions of Hell to bring about The End of the World as We Know It. Unfortunately, he keeps getting his face rubbed in these things until he grudgingly starts to believe.
By The Last Hero, Rincewind has become Genre Savvy enough to know when he's likely to be drafted for the Disc's first space flight, and grudgingly volunteers in order to save himself time trying to hide from The Call.
Jonah in The Bible is an example of Resigned To The Call coming after he Refused The Call and got a dose of You Can't Fight Fate. By the time the big fish spat him out, his attitude had changed from "I am NOT going to Ninevah!" to "I guess I'm going to Ninevah."
Moses too. His response to his God is a) Why me? b) what do I say when they ask Who sent me? c) You know they're not going believe me. d) I'm a lousy public speaker. Until God loses his temper and tells him to stop whining and don't keep his brother Aaron waiting!
(Bel)Garion, the main Chosen One of David Eddings' Belgariad is Resigned To The Call; he spends roughly 4 1/2 of the five books asking "Why me?". C'Nedra also spends a fair bit of books 4 and 5 Resigned To The Call, giving recruiting speeches and leading the army because, according to the Prophecy, she must in order for Belgarion to have a chance to win.
Morgon of The Riddle Master Trilogy is very much not happy about the ambiguous, threatening prophecies that have been ascribed to him and only grudgingly agrees after almost being murdered a few times to try and figure some of this stuff out.
In Kingdom Keepers, the keepers aren't to enthusiastic about their new mission, especially Maybeck and Charlene. However, since they cross over every time they fall asleep, there's little they can do except go with it.
Aislinn in the Wicked Lovely series. She realizes that she has no choice about being a faery, but she makes clear that she will only do it on her own terms.
In Tolkien'sFarmer Giles of Ham, Giles doesn't really want to go dragon-hunting, but he knows he will eventually have to and can't keep making excuses for ever.
George Powhatan of The Postman answered the call once before, fighting off vicious survivalists to establish his own small farming community. When Gordon arrives seeking help for the beleagured Willamette communities, George tries Refusing the Call, but the fact that this is listed on this particular page should tell you how well that works out.
Similarly, Stannis Baratheon doesn't really want to succeed Robert as king. However, it's his duty to do it and thus he will, even if it means rebelling against Joffrey and fighting the Lannisters, Starks, and most of his own bannermen.
In The Lost Fleet, Captain John "Black Jack" Geary has been put in command of the crippled Alliance fleet against his will (being a Human Popsicle for 100 years gives him seniority over any other captain). He vows to bring the fleet home, but then wants nothing more than to retire and live in peace. By the end of the main series, he realizes that the Alliance desperately needs him, and he can't quit.
On average this seems to be the attitude of the Oceanic Six returning to the Island on LOST, especially Hurley. The clearest exception is Sayid, who had to be dragged in handcuffs.
The attitude of one Buffy Summers throughout the majority of the series. She tries to refuse the Call at various points, especially at the beginning, and the hope she feels when other Slayers start showing up is just heartbreaking when it becomes clear that she can't just step down and let the new Slayer take over. She also implies, at various points, that the job itself is pretty cool - her objections to it are based in the masquerade killing any chance of hereverhaving a normal relationship - or in some cases any relationship (count her exes, folks: Angel (vampire); Riley Finn (super soldier); and Spike (vampire) and a string of normal men) and the fact that "retirement" means dying. Also, the Call keeps dragging her friends and family into the mix, which she really objects to. Plus, by age 18, she's one of the oldest slayers ever (by the end of the series when she is in her early 20's, she's the oldest slayer in history) and she's been revived twice.
In the episode where she has Spike tell her about how he killed two previous slayers, he argues this trope is what truly kills them; they may start out fighting for survival, then fight to protect other people, but eventually they accept their destiny (and the extremely short life-span involved) and become death seekers. Once that happens, it's only a matter of time until some vampire or demon gets in a lucky shot.
Tenkaichi from The Conditions of Great Detectives says that he hates being a detective but since he has no choice in the matter he's determined to do it right and since he's the only one who can do it he becomes rather proud of it (while still hating it).
Ziggy of Power Rangers RPM. The only reason he's Series Green is because he had to morph to keep the Morpher out of Tenaya 7's hands and since it's DNA-locked, he can't just fork it over to someone else instead.
The main character of Brand by Henrik Ibsen is a priest (which usually has the "call" as a job description). When he eventually takes the job, it is with great reluctance, and arguably for the wrong reason (not for The Needs of the Many, but to save his mother). He is quite resigned to the call all the way, but the trope is zig-zagged because he actually thinks he has a calling, he just doesn`t want to do it like that, and not at all in that exact place, which he detests.
Reimu Hakurei of Touhou is a bit of a hypocrite as far as this trope is concerned. On the one hand, it's her job as the local shrine maiden and Youkai Exterminator to take care of the incidents that turn up in Gensoukyou. On the other hand, she is a lazy bum who'd much rather stay at home and wait for the problems to work themselves out rather than go out and actually do something about them. On the third hand, she will, however reluctantly, go out and take care of an incident if she gets bored with the peaceful tedium of her humble abode. And on the fouth hand she'll start complaining if life gets too peaceful and boring, so yeah. Meet our Heroine, folks.
After a few quests in Fallout 3, you start to get dialogue options that suggest (if you choose them) that the Lone Wanderer is becoming resigned to fixing everyone's problems, such or "I can see where this is going..." or "So, you want to do it?"
Corrine "Merlynne" Bertrand is the product of a prophesy thousands of years old. Her family was off-the-rails crazy, with a mother who perpetuated unbelievable levels of abuse to try and "protect" her children, and a father who was into Black Magic and the occasional summoning of an Eldritch Abomination now and then. After an accidental manifestation of her abilities destroys the family home and a few family members, Corrine runs away, embraces Christianity (which fulfilled part of the prophesy on her family), and was found by Dr. Fate, who helped her control her magic. She remarks frequently that it's a wonder she's anything resembling sane. As much as she would like NOT to be a Chosen One, she realizes one of her insane family members could always assume that mantle if she doesn't.
Caleb and Amelia Zukov are descendants of the succubus Chantelle (from Hellblazer). Caleb accidentally put his sister into a coma, and learning to use his magic was the best chance he had to revive her. By the time he did manage to wake Amelia up, he was already a former member of the JSA and current member of the Outsiders. When Amelia woke up, she only went along with the Outsiders to be close to her brother. After falling out with them, she had enough of a thirst for adventure to get in with a revival of The Elite.
Tara "Green Shield" Strong was a pharmaceutical chemistry student who was diagnosed with a rare, terminal neurological disorder. She experimented on herself only so that her research would support her family, sparing them the horrendous medical bills her conditions would eventually lead to. The bad news was that her boss stole her work. The good news is that her plan to inject herself with the chemical and use her own body as a smoking gun not only retarded the progression of her illness, but granted her enhanced strength and durability. After literally stumbling into the middle of an attack on Clan Arrow by Cheshire, she took the offer to train with them because she still, on some level, believes that she will die soon.
Aurora "Fauna" Andersen was a Granola Girl activist, and raised as an Actual Pacifist, even supporting a movement to make superhero work illegal...until she led a protest outside of LexCorp HQ. For reasons she can only speculate on, she was kidnapped by Luthor's thugs and subjected to medical torture that left her with animal-based shapeshifting abilities, along with some pretty nasty side effects. After escaping, she got a job at Black Canary's flower shop, and was literally recruited into the Titans on a phone call. Even though it betrayed her upbringing, Fauna threw her lot in with the capes because the alternative was a life constantly running from Lex Luthor.
The star of The Life and Times of Juniper Lee. She has the role of the Te Xuan Ze imposed upon her whether she likes it or not, but once engaged in her role as the balancer of the real world and the world of magic, Juniper performs it with gusto.
How many in the military look on the various hardships or inconveniences they might find themselves enduring (deployments away from family, the sometimes harsh lifestyle, dubious chow hall food, and the occasional draconian or misguided policy from higher up). A viewpoint expressed with the acronym BOHICA (Bend Over, Here It Comes Again)
Pope Benedict XVI had planned on retiring for a while before he was elected Pope. He also admits to having prayed to God "Please don't do this to me!". He eventually became only the second Pope in history to resign.
Kim Il Sung supposedly preferred being a military man over a political leader, at least according to the Soviet Diplomats who had to convince him to take up leadership because he was the closest thing to a Communist leader in Korea following the Japanese occupation.
Upon being elected President, George Washington told a friend that his feelings on traveling towards the capitalnote which at that point was New York City; Washington actually took the oath on Wall Street, right next to where the Stock Exchange now stands, and where Federal Hall was later built in his honor for his inauguration were rather like those of a criminal traveling to the gallows.
C.S. Lewis describes his conversion as this in Surprised By Joy:
You must picture me all alone in that room in Magdalen, night after night, feeling, whenever my mind lifted even for a second from my work, the steady, unrelenting approach of Him whom I so earnestly desired not to meet. That which I greatly feared had at last come upon me. In the Trinity Term of 1929 I gave in, and admitted that God was God, and knelt and prayed: perhaps, that night, the most dejected and reluctant convert in all of England.