Reluctant Monster

"I'm just a shade shy of true wickedness
I'm just a shade shy of truly loving this
Yeah, there are other things I'd rather be doing
Even nothing."

—The Tragically Hip, "Family Band"

The Reluctant Monster (usually) has no idea that they're a monster. They're a member of a species that traditionally does nasty things to people, but for them it just never crossed their mind. Folks tend to scream and run away, which is rather disheartening and lonely.

In darker stories, people will try to kill them, and it's easy to fall into depression. Occasionally there are other, more traditional members of their kind who do terrorize humanity, but the Reluctant Monster's mild temperament sets them apart from their own kind just as much. In more traditional groups, they're the Minion with an F In Evil.

True heroes look past appearances and befriend them, even advocating better treatment. Usually, The Chick notices they aren't attacking and discovers their true nature.

The very extreme of My Species Doth Protest Too Much. If the character is of great size, they may be a Gentle Giant. If they're "ugly", they might be a Gorgeous Gorgon. Compare Non-Malicious Monster and Monster Adventurers. Likely to result in Van Helsing Hate Crimes.

Examples of Reluctant Monster include:

Anime and Manga

The "Fat Buu" incarnation of Majin Buu from Dragonball Z is an enormously powerful, childlike, playful, generally friendly creature that only causes mass destruction because he was ordered to by his creator; the character of Mr. Satan is able to reform Buu simply by informing him that it is wrong to kill and asking him not to do so anymore. Much later, after the Big Bad has been defeated, the people of Earth shun Buu, citing the worldwide devastation he caused prior to his Heel Face Turn; this forces the Z Fighters to erase Buu from the memories of everyone on the planet so that he will be able to live among them.
Seras Victoria of Hellsing, is fully aware of her condition, but she does her best.
Another ghost who is barely aware of it, Aisaka Sayo from Mahou Sensei Negima. The manga version is a Dojikko who manages to trip over her own feet despite not actually having feet. The anime version gets an entire episode.
An earlier example, the Ranma ½ anime has Kogane, the least frightening of all the various monsters, spirits and demons that have shown up (a list that includes, but is not limited to, a pair of giant, but harmless, jellyfish, a badly drawn female panda come to life, an evil spirit that possesses people to feed on their evil impulses and their life-force, a hideous horse kami and his equally ugly boar kami friend, the Orochi and a demonic cherry tree). She does have Ghostly Goals... finding a tanuki doll she forgot to pick up when she bought the notebook that her spirit is anchored to you, and is so shy and retiring she bursts into tears when Nabiki demands to know what she wants (quoth Kasumi; "Nabiki, please stop scaring the ghost").
Maya the Phantom Cat from Geobreeders.
Ichiko from Otome wa Boku ni Koishiteru. The main character has a hard time convincing her that she's a ghost, despite her constant floating, not to mention the fact that she hasn't aged in about twenty years, during which she's been living in a closet (although certainly not in the closet).
Young Gaara from Naruto fits this trope to an extent as he holds within him a monster but is quite a kind and helpful person... who everyone runs away from screaming. This further upsets him and makes the sand react in a dangerous manner, reinforcing the fear. An attempt made on his life by the only person to have ever shown him kindness causes him to snap and embrace his monstrous side.
Shia from Pita-Ten. Worst...demon...ever. She's nicer than the angel. Than most angels. Her Right-Hand-Cat is embarrassed. This has disastrous consequences, much more so in the manga.
Nel from Bleach, a pacifistic Arrancar, and is pretty much a child. She ended up helping Ichigo not out of revenge to Las Noches due to being the former third Espada, or third-most powerful Arrancar, but because she liked Ichigo and simply got caught up in the battle.
Misaki from Blood Alone is a completely innocent little vampire girl. At her worst, she's a pouty Clingy Jealous Girl.
Shades of this, mixed with Bad Powers, Good People, color the God of Poverty in Kamichu!!.
Ryner Lute from The Legend of the Legendary Heroes is constantly labeled as a monster because of his Alpha Stigma, a power which eventually goes out of control, destroying everything around it and killing the user. However, he rarely uses the Alpha Stigma outside of battle.

Comic Books

The stupid rat creatures in Bone argue about whether they should act like monsters or not, and on occasion try to get out of trouble by telling the good guys "It's not our fault we're monsters, we were born this way!"
Bizarro is often written as possessing all of Superman's heroic tendencies, but with such a... well, bizarre view of the world that his attempts to express them only cause disaster.

Fan Works

Nightmare Nyx from the My Little Pony: Friendship is Magic fic Past Sins. She knows she's been turned into a monster, but she doesn't want to be, desperately tries not to be, and actually doesn't do too bad a job as queen of Equestria, after a few false starts.
- Grown-up Spike in It Takes a Village. His friends and all of Ponyville see the same little dragon who grew up around them. The neighboring communities don't. No matter what his fellow dragons say about him.

Film

That one alien in Aliens in the Attic.
Possibly the eponymous monster in Cloverfield. According to the producers, Clovie was given a rude awakening by a falling satellite and was more disoriented and grumpy than actually malicious. He's also supposed to be a baby, and so the whole movie could just be considered the result of a kaiju temper tantrum.

Literature

The Reluctant Dragon is an 1898 children's book by Kenneth Grahame (originally published as a chapter in his book Dream Days), which served as the key element to the 1941 feature film with the same name from Walt Disney Productions.
In the Cineverse Cycle, Book Two, the Slime Monster doesn't really like scaring people. His name is Edward and he is simply very misunderstood.
The various Frankenstein films have often portrayed the monster who acts as a main character as a confused beast who doesn't want to hurt anyone and is unfairly hunted down by the villagers. In the original novel, the monster was like this at first, but after being hunted wherever he is found, he vows revenge on his creator and kills Frankenstein's brother, friend and wife. At which point Frankenstein becomes the hunter.
The title character of The Big Friendly Giant.
Discworld:
- Reaper Man features a boogeyman who is actually very agoraphobic and vastly prefers hiding behind things over jumping out from behind them at people. He gets better just in time for a Big Damn Heroes moment, where he saves everyone from a sentient shopping mall.
- Unseen Academicals has Nutt, an orc pretending to be a goblin-thing because of the stigma surrounding orcs. (Orcs were created by an Evil Overlord to be used as super-soldiers in some war.
- The Watch books have Angua, a werewolf who is really quite civilised and hates the monstrous members of her race.
While no creature in the British Aerial Corps are more vicious than any man, Temeraire in particular seems frequently befuddled and occasionally offended concerning how readily most humans are frightened by a barn-sized predator with sharp claws the size of a woman's forearm and a maw that can devour a cow in three bites.
The main character in H.P. Lovecraft's "The Outsider" is one, if only for a minute. He spends most of his life completely alone, thinking he's human. When he finally does meet other people, they run away in terror, and he even terrifies himself when he sees his reflection. He quickly decides to just go with it.

Live-Action TV

Barney the Dinosaur. He's a Tyrannosaurus, and has not once in the show's fifteen-year run tried to eat the children or Baby Bop. Instead, he'd rather play make-believe and sing.
- Yet
Cirque Du Soleil's Widget Series Solstrom played with this via a Metamorphosis—in the horror pastiche "Howling Wind", a hotel is transformed into a Haunted Castle / Hell Hotel hybrid via magic. While surprised, the elderly Hotel Owner decides to go on with business as usual as best he can, and thinks nothing of (if he even notices) the help being transformed into ogres, vampires, and sundry eccentrics, or even that Death is now a guest. As it turns out the magic is slowly turning him into a Wolf Man. But he's hardly aware of his increasingly monstrous form—when he notices that his fingernails are turning into claws, his response is simply to try filing them down. So preoccupied is he with being a good host that it's a shocked guest whose reaction alerts him to the fact that he's grown a tail. In The Stinger, the transformation is complete but he is still affable and harmless.
The TOS Outer Limits episode "Behold, Eck!" was originally titled "The Reluctant Monster". The titular creature is a meek, polite two-dimensional being from Another Dimension who accidentally winds up in our world and wreaks unintentional havoc while the heroes figure out how to send him home.
Sesame Street is prone to use characters with "monster" in their names, but these characters are invariably harmless.
Possibly Amy from Supernatural. She didn't want to be a kitsune and even killed her mother to save a younger Sam from her. Sam in turn saved her from John and Dean, who were on the hunt. She was only killing to save her son, who was sick. Then again, it's left ambiguous whether or not this is really the case. Dean kills her rather than wait to find out.
The Munsters: They're monsters ripped from the old Universal Horror movies, but they act as a fairly typical, if eccentric, working-class family that can't understand why most strangers seem to turn pale and run whenever they see them.

Mythology

In Ovid's telling of Medusa, she was a beautiful maiden who laid with Poseidon in Athena's temple. In some tellings, she's raped. For this "offense," she's cursed by Athena with living serpent hair and a terrible visage that would turn men who looked upon it into stone. Thus, Medusa's powers are unintentional and unwanted. Perseus, who eventually kills her, believes that the punishment is well-deserved. The trope is averted in earlier myths, however, which describe Medusa as one of three monstrous sisters, the Gorgons. Perseus kills Medusa simply because she is the only mortal Gorgon.

Tabletop RPG

In Promethean: The Created, this effect is called "Disquiet", and affects all of the Frankensteinian heroes—people will eventually turn on them no matter where they go.

Video Games

Vivian the Shadow Siren from Paper Mario: The Thousand-Year Door is a rather friendly creature of darkness (possibly even a demon of the same race as the Shadow Queen) who joins Mario's party.
Most video games in the Atelier series by Gust (of which the Atelier Iris games are but a small part) feature a ghost named Pamela who either does not know she is a ghost or is oblivious to the fact that people find her scary.
A quest chain in Final Fantasy Tactics Advance 2 begins with a mission where the player must bring a potion to the client. It turns out that the client is a zombie and doesn't know it; it's not aggressive though, and upon being informed of its post-life status, it sadly shambles off into the mist. The rest of the quest chain reveals that the zombie is Frimelda, a legendary swordswoman, and completing the quest chain cures her zombification and lets her join the player's clan.
Fawkes in Fallout 3. After much time splattering the brains of Supermutants across the wasteland, the player encounters a genetic experiment gone wrong in cell 5 of an abandoned Vault, a nod to V for Vendetta - the name even refers to Guy Fawkes, the Catholic restorationist whose face is the template for the mask V wears. (S)he knows (s)he is a monster, but while the FEV that created all supermutants made most of the rest of Supermutants hulking bloodthirsty monsters with the IQ of a vegetable, Fawkes is intelligent and has a good heart, and offers to help the player in their quest.
- There's also Uncle Leo, the friendly Super Mutant who wanders the wasteland.
In Okami, the imp merchants only want to sell you something - even when you attack their bases.
Touhou is filled with creatures with quite nasty traits and histories, but the days of animosity between humans and Youkai are long gone and the denizens of Gensoukyou are more interested in parties than following past trends. Even Remilia, local vampire princess who boasts about being a terror of the night, never drinks enough blood in one sitting to kill anyone and the worst thing she ever did was block the sun for a while so she could go flower viewing during the day.
In Shadows of the Damned, the traveling trader Christopher is a monstrous looking creature with a Slasher Smile, who tells you he is half man, half "beast". When Garcia, the main character, calls him out on it, Christopher shoots back with, "you gotta look past the leath'ry exterior! Deep down I am a sensitive and understanding listener!"
- He even surrounds himself with flower gardens and lamps, the latter of which keeps hell's demons away. How sweet!

Web Comics

A bit of a subversion occurs with the Monster in the Darkness from Order of the Stick. He knows he's a monster (although even he's not sure what kind) and incredibly dangerous (he knocked one character and her horse several miles when trying to hit as lightly he could), but is so innately sweet-natured that he is horrible at being monstrous and could even be considered to be somewhat helpful to the Order of the Stick.
The title character of George the Dragon has a steady diet of junk food and can't even eat a hamster, never mind a human. (And set a bunch of food-type hamsters free.)
Buwaro of Slightly Damned just wants to give the world a big hug. However, being a member of the vicious and powerful Demon race makes most people more likely to scream in terror.
Done in reverse during the "That Which Redeems" arc from Sluggy Freelance. When people from the Dimension of Lame are transformed into demons, they readily identify themselves as evil, but because of how ridiculously pure and good-natured they were to begin with, their idea of "evil" is making scary faces at young children.
In Succubus Justice, the Villain Protagonist, Karina, is attending a school for the purpose of correcting her Minion with an F In Evil personality.
Daniel Ti'Fiona from Dan and Mab's Furry Adventures doesn't want to be an incubus. This is both Played for Laughs and Played for Drama.
Schwarz Kreuz's main character, Nikolas Von Helsing. He's a descendant of that Von Helsing. He used a ritual to turn himself into a vampire when his group of Paladins/Clergymen was under attack by Nazis, and thus manages to survive to continue his order. Doesn't drink blood, but does drink alcohol. Lots of it.

Western Animation

The title character of Casper the Friendly Ghost, and his pal Wendy.
Loopy de Loop, a wolf character from Hanna-Barbera.
Tiger, the cat Fievel befriends in An American Tail.
The title character of Shrek, more cynical and self-aware than most, is fully aware of his species reputation; he just wants to be left alone.
In Monsters vs. Aliens Susan Murphy grows to a height of almost fifty feet after being stuck by a meterorite. She is quickly labeled a "monster" by the government and is put in a detention facility, despite not doing anything malicious or intentionally destructive at all. She is joined by her fellow inmates Doctor Cockroach, The Missing Link, B.O.B., and Insectosaurus.
This trope is played hilariously straight in Robot Chicken.
Roger the Alligator, from The Penguins of Madagascar. A notable aversion of Reptiles Are Abhorrent, he is extremely pacifistic and would rather bake muffins for his enemies than hurt them.
Aqua Teen Hunger Force has an onion-bodied spider named "Willie Nelson" who lives in the Aqua Teens' attic. He's very mellow, except for when he's actually in the attic.