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Kurokami Medaka from Medaka Box. Medaka denies it of course. Later, it is implied that she may have dropped her paragonic tendencies.
Kamina from Tengen Toppa Gurren Lagann, while widely recognized as a hero, mostly sought to bring out the heroism in other people. Having self-confidence rather than relying on a hero is actually a major theme in the series.
Ironically, he is also somewhat of a subversion because he didn't really have much self-confidence himself. He just played a good show of it and relied on Simon.
Indeed, it gets obvious that while Kamina was a paragon to both Simon and the whole Dai-Gurren Brigade, Simon was just as much of a paragon to Kamina, both relying on each other's support to be able to do good. Kamina's death later on was one of the main reasons Simon learned to become a true hero, stating that he still lives on in his heart. Kamina did, in fact, put up most of the show in front of Simon to inspire him to true heroism.
Hakuoro in Utawarerumono. His opposite number actually gets sort of pissed at him for teaching the people all sorts of things and rapidly advancing their civilization, the logic being that it will create more conflicts. Inventions shared: Agriculture, steel production, teaching people to lead their own countries, medicine, modern chemistry, etc. Note, shared. He teaches the people to make these things for themselves.
Subverted with Griffith in Berserk. He's introduced as a very charismatic person and he seems to be a very good example of this in how he raises up the members of the Band of the Hawk. In particular, in his first meeting with Casca, he gave her a sword to kill her attempted rapist, and he helps transform Guts from a brute into a thoughtful soldier. However, he ultimately seems to only view others as pawns and in his epic Face-Heel Turn during the Eclipse, he betrays the people he previously motivated in the most horrific way possible.
Nanoha fits this pretty well. She befriends several Anti-Villain characters, and does her best to show them that there are better alternatives. In the third season and after, she becomes an instructor in magical combat, as she has come to the conclusion that the way she can help the most people is to pass on the skills and knowledge that she has acquired.
Ironically, Vegeta wants to invoke this towards the end of the Dragon Ball manga. When Goku suggests that Gotenks or Gohan (both of whom had surpassed Buu at that time) should just come and kill Buu, Vegeta tells him that it's now humanity's turn to shoulder some responsibility and has all humans share their energy with Goku so he can blast Buu with an enormous ki attack.
Touma Kamijou from A Certain Magical Index seems to have an unconscious gift for turning the people around him into heroes. Most people he defeats eventually become inspired to do the right thing, using him as an example.
Spider-Man, in addition to being one of the most morally upright characters in comics, is pretty much this for the concept of "self-sacrifice". One comic has a darker version of this, beginning with a mugger killing some woman in an alleyway and a Punisher-style vigilante promptly killing the mugger. Spider-Man put him in jail, of course, and remarked, "What was he trying to do, anyway?" The answer is covered in the bookend — this time, a woman targeted by a mugger draws a knife and kills the mugger.
Captain America, what with his incorruptible moral purity and all. This actually became one of the problems with Civil War: Whether the Pro-Registration side was in the right, or if they were going for something more gray-area, they put Cap on the anti side, so most readers, and some writers, naturally assumed they were the Good Guys.
In both the Superman movies and the The Dark Knight Saga, this is the heroes' goal. (Although in The Dark Knight, Bruce expresses disapproval of the groups of men who dress like Batman in groups, A. because they often get hurt or killed, and B. because they use guns.)
Spider-Man Trilogy: Though he doesn't set out with this as a goal, Spider-Man tends to succeed at this at least Once Per Movie, typically with nearby New Yorkers not known for their friendliness working together to save his life or even fending off some rather nasty villains.
Computer Tech: ...I'm sorry, sir. I can't launch those ships. Captain's orders. Rumlow:[draws gun] Step away from the console. Agent 13:[as she and everyone else draw their guns] You heard him. Captain's orders.
Folklore and Mythology
This is practically a Universal Trope in Mythology. Without someone to aspire to be like, it's hard to worship anything.
The Istari in The Lord of the Rings were meant to be Paragons: "It was afterwards said that they came out of the far West and were messengers sent to contest the power of Sauron, and to unite all those who had the will to resist him; but they were forbidden to match his power with power, or to seek to dominate Elves or Men by force and fear." In the end, only Gandalf truly fulfilled this role.
However letters Tolkien wrote towards the end of his life claim the two Blue Wizards were stirring up rebellions against Sauron in the East, which prevented his forces outnumbering those fighting him. And other notes of Tolkien imply Radagast was sent to protect the nature of Middle-Earth.
In the H.I.V.E. Series, HIVEmind grows to fill this role, eventually sacrificing himself so that Otto can kill Overlord and get home safely.
H.I.V.E.mind: You are as strong as you wish to be.
And Karrin Murphy, a policewoman and voice of morality to the protagonist, is also an example. Really, any Knight of the Cross is expected to be a paragon; it's basically their job to help people in need and battle evil. (If any Knight tells a lie or breaks a promise, the mystically-empowered blade they wield actually has a chance of breaking.)
Many of Tamora Pierce's Tortall heroines are this, particularly Alanna from Song of the Lioness. She even says in the third book, Woman Who Rides Like A Man, something to the effect of "If I waited for things to change, they never would have," as an explanation for why people should work for change. Her success inspires numerous girls in and out of Tortall, and her Badass Normal successor Keladry from Protector of the Small inspires even more.
Superman in The Reckoners Trilogy. Note that Superman doesn't actually exist in this universe. But in a world where every superhuman is, without exception, a sociopathic mass-murderer, some people still carry around his S symbol under the firm belief that some day, heroes will come. It's the closest thing to a religion left.
Live Action TV
The sinister group of shady conspiracies, called The Syndicate in The X-Files views Fox Mulder as The Paragon of an ever-growing movement of conspiracy theorists-slash-whistleblowers (part of which are characters like Max Fenig and the Lone Gunmen). In fact, the main reason why they don't just shoot him is the fear that a dead paragon would become a banner to rally all the tinfoil-wearing nutjobs to start digging everywhere and eventually discovering their existence. Ironically, Mulder himself is hardly aware of this special status until well into the series.
In Once Upon a Time, Emma's dubious about Henry calling her The Chosen One, but she is racking up an impressive record inspiring the cowed townsfolk into standing up for themselves and making their own "happy endings."
In The Twilight Zone 2002 episode "Azoth the Avenger Is a Friend of Mine", the hero Azoth the Avenger encourages a boy to be brave enough to stand up to his abusive father, instead of relying on him to solve all his problems.
The other swordswoman from Heather Dale's song, "One of Us".
Table Top Games
The Unconquered Sun functions as the Paragon of all Virtues, and exists as an ideal for all other beings to strive towards. Interestingly, his creation as The Paragon was intended by the Dragon's Shadow as an instrument of evil; his ultimate Virtue allowed the Dragon's ultimate evil to have something to define itself against, and his endeavors for people to emulate him gave the Dragon the opportunity to be against lots of people at once. This didn't work out well for the Dragon.
Even Warhammer 40,000 has one in Sanguinius, Primarch of the Blood Angels. Though his brother Horus was put in command of all the Imperium's forces, as Horus lay dying, he remarked "Sanguinius. It should have been him. He has the vision and strength to carry us to victory, and the wisdom to rule once victory is won. For all his aloof coolness, he alone has the Emperor's soul in his blood. Each of us carries part of our father within us, whether it is his hunger for battle, his psychic talent or his determination to succeed. Sanguinius holds it all. It should have been his."
The Avatar in the Ultima games. This was explicitly the plot of #4.
Depending on the ending, you turn out to be this kind of guy in Baldur's Gate: Throne of Bhaal. In the good ending, it is specifically mentioned that you'll end up spawning a host of imitators.
In Dragon Age, Dwarves that distinguish themselves with truly awesome deeds and/or inventions are literally called Paragons. Revered as "Living Ancestors" (the Dwarves worship their ancestors instead of gods and regard Paragons as such whether or not they are actually dead), the Paragons are meant to serve as examples for Dwarven society to follow. The most recent Paragon Branka, for example, earned her status by inventing smokeless fuel which burned hotter and cleaner, simultaneously boosting production and reducing things like black lung. The Paragon Caridin earned his rank by building the Anvil of the Void, the key to creating Golems. To gain the allegiance of the Dwarves, you have to get one of these Paragons to help you settle the Succession Crisis over Orzammar's throne. At the end of the game provided you are playing as a Dwarf and didn't sacrifice yourself to slay the Archdemon, you become a Paragon. If you sacrificed yourself, you become a Paragon posthumously.
Turning the main character into this is the end goal in Zettai Hero Project. Starting off as a spineless bystander, he ends up helping the people help themselves and inspiring the entire world into not giving up hope against the Final Boss.
As an aside note, he was actually a Crouching Moron, Hidden Badass BEFORE he got the belt, having protected his little sister at the age of 8 by being a meat shield from a cannibal/rapist/killer. The only reason he seems spineless is because of a HORRIBLE home life that basically snuffed his Heroic Spirit down to a tiny ember.
Garlot (Gulcasa)'s usual messianic behavior verges on this at certain points of Blaze Union, especially when the mission of the day involves lecturing some sense into the local townspeople (as in the battlefield "Waves in the Grain") or a despairing teammate. This is a kind of inverse Cerebus Retcon — Yggdra Union demonstrates that all of his allies and the citizens he winds up ruling are all willing to follow his example and take up arms for him and Bronquia in times of need in the most depressing way possible; Blaze Union is just going back to explain how this came about.
In Mass Effect, Commander Shepard can fit this trope depending on some choices made. Actions and dialogue choices include as much you resolving the situation as prompting others to get out and make a difference on their own. News reports after particular Paragon events often report how your influence has inspired those you met to do the right thing. Other examples include Captain Anderson and (for a Krogan) Urdnot Wrex.
Wrex is noteworthy in that he had attempted to be a Paragon long in the past, but gave up. He tried to guide his people towards a path of rebuilding and reclaiming their world, but his own father tried to kill him for it. If he lives through the first game, Wrex establishes himself as a progressive clan leader with immense influence over the other clans.
If you honestly assist him in the third game, Wrex (and Bakara) become the paragon leaders for all the Krogan.
It's worth noting that the game's morality system literally refers to this particular style of action as "Paragon". (Actions taken from a more pragmatic mindset are called "Renegade".)
In Fire Emblem Awakening, Emmeryn fulfills this role when she throws herself off the cliff in Chapter 9, inspiring much of the Plegian army to desert from King Gangrel's plan to destroy Ylisse.
The Guild Wars expansion, Nightfall, adds the Paragon profession- more often than not, the Paragon is used less for the martial skills and more for their party-wide buffs, so it could be argued that the Paragon uses his speech to inspire his allies to be the best they can be.
Vyse, The Hero from Skies of Arcadia, fits this trope so well that he may as well just marry it. He pretty much convinces everyone in the entire world to fight against Lord Galcian and Valua by the end of the game. Seriously, Gondor Calls for Aid taken to it's greatest extreme, and he doesn't really "call" as much as "everyone turns up and asks if they can help out".
In Tin Star (Choice of Games), in the epilogue, your actions and personal Karma Meter will influence the character and actions of the people you met during your time in Lander County. This means if you consistently acted with honor, upheld the law and maintained public order, people around you will take the lesson to heart; you can even get a character canonized as a saint for their virtues.
Princess Cadance does this for the Crystal Ponies in My Little Pony: Friendship Is Magic, who were too thoroughly broken by King Sombra's tyranny to resist him. After recovering the crystal heart, she offers it to them and rallies them to use it's power to defeat Sombra once and for all.
Princess Cadance: The crystal heart has returned! Use the light and love within you to ensure that King Sombra does not!