Since it takes place in the world of fairy tales, it is no surprise that plenty of characters in MÄR are parodies or Captain Ersatzes of fairy tale characters. This page is an attempt to chronicle the various references.
Both being very adventurous and Ginta often saves Dorothy and Snow from harm. Babbo has the more gentleman aspects of the character trope, being polite, flirtacious and honourable.
In the first episode/chapter, Ginta dreams of rescuing Koyuki from a demonic king, and is of course summoned to MÃR Heaven to defeat the evils there - just like several princes in fairy tales who are summoned from distant lands.
Some of Babbo's alternate Ãrm forms symbolise fairy tale characters, namely his fourth form Alice, clearly inspired by Alice in Wonderland, and sixth form which stems from Puss in Boots.
Princess Snow is the princess of Lestava, and, by extention, pretty much all of MÃR Heaven. She also happens to share traits with a number of fairy tale princesses, namely:
Snow White: The secret is in her name. In addition to the name, Snow is being pursued by an evil queen, she ends up frozen in a block of ice, which is visually similar to Snow White's clear coffin from her story, and she is kissed by Ginta about the same time that she wakes up from her frozen sleep (it's not because of the kiss, but still). Also, she fights a chess piece that asks her magic sword "who is the fairest one of all?"
Sleeping Beauty: As mentioned above, she is locked into frozen sleep, and is kissed by Ginta at about the same time she wakes up. She is also being persecuted by an evil witch.'
Oh, and for bonus points: The evil queen, evil stepmother, and evil witch? All the same person.
The anime adds one more, whether it was intentional or not. At the end of the original Brothers Grimm book, Snow White and her beloved prince go off together into the sunset to live happily ever after together. At the end of the anime, Snow and Koyuki have merged into one person on Earth to be with Ginta. Their final scene together is walking home together AT SUNSET, their arms linked and blushing. There's nothing stopping them from being together anymore, it's a fitting end.
At first glance, prettyboy Alviss may not seem like a fairy tale parody, but a few things about him all point to a sly reference to Peter Pan
He is the one who brought Ginta into a fantasy land, like Peter did for Wendy
His constant companion is a jealous fairy named Belle.
He is the one to effortlessly defeat the pirate-themed Chess Piece Mr. Hook.
He is infected with the Zombie Tattoo, and if it is allowed to finish spreading, he will be rendered eternally young, unable to age or grow. Unlike Peter, Alviss does not consider this a good thing.
His dream is to one day grow a beanstalk like the one seen in the fairy tale, large enough to reach into the skies.
Once he gets some better magic power, he starts using a wide variety of magic beans and seeds. Well, actually, he uses magic beans from the very start; special beans that grow into edible food overnight, just like the kind that the fairy tale Jack thought he had bought.
He's not a fairy tale parody, but a favorite fan theory is that Nanashi is literally the character Joker from Anzai's other manga, Flame of Recca. The evidence for it is as follows:
Babbo noted that Nanashi has the smell of an otherworlder about him.
He displays the same impressive increase in strength that otherworlders have in MÃR Heaven.
When Joker disappeared from Flame of Recca, he had a nasty stomach wound. When the Luberian Thieve's Guild found Nanashi, he had that same wound, and Joker's clothes, and amnesia.
Joker did not die "on screen" in Flame of Recca, he was sucked into a black hole, which could very well have been a sort of wormhole that pulled him into MÃR Heaven.
While Alan does not appear to really be inspired from any fairy tales, his name may be a nod to Alan Garner, a British novelist who wrote several fantasies and fairy tales.
He may be inspired somewhat by Ichabod Crane from The Legend of Sleepy Hollow, due to his intelligence, and relationship with Halloween.
And the entirety of Team MÃR is a further Snow White reference, as a Lestavan fortuneteller told Snow to seek out the "Seven Dwarves" who would save MÃR Heaven. Snow plus the seven others (Ginta, Jack, Dorothy, Alan/Edward, Alviss, Nanashi, and Babbo) makes "Snow White and the Seven Dwarfs".
Dorothy's older sister and queen of the Chess Pieces, Diana mostly draws from the Evil Stepmother from Snow White and Cinderella.
She threatens to kill Snow who flees with Edward.
Diana goes more insane over time, demanding the most beautiful things in the world to be hers - remiscent of the evil stepmother's desire to be the fairest one of all.
Diana uses reflective surfaces to view other parts of the world, a nod to the Magic Mirror in Snow White.
Diana may also originate from the Wicked Witch of the West from the Wizard of Oz, due to her relationship to Dorothy and being a witch.
Phantom is a tragic figure in his own right: Corrupted by the Caldia's Orb, and sentenced to death which his parents were meant to carry out but they were Driven to Suicide. The Phantom suffers a similar fate where he is persecuted due to his deformed appearance.
Phantom's alternate identity Tom may stem from Tom Thumb due to his false kind persona, and how an early myth regarding the character was used to frighten children and deceive them.
Her main weapon is the Ärm "Hair Master", which allows her to manipulate her hair as a weapon. A reference to the fairy tale character's long hair, which people used as a ladder. Funnily enough, this one does not have Rapunzel Hair, but rather has it all bound up into a massive Beehive Hairdo.
In the fairy tale, Rapunzel was locked in a tower by her wicked mother figure (having been given away to the witch by her real mother). In MÄR, Rapunzel and her brother were also abused by their mother figure. So they killed her with an axe.
Lesser Chess Pieces
A lot of the low-rank Chess Pieces (Bishop and lower) who only get one fight scene are one-note references to fairy tales. They include:
Alibaba. An Arabian-styled chess piece whose main Ärm (A Guardian called the Genie of the Lamp) marks him as an obvious reference to Aladdin. He was an overconfident blowhard who thought that his guardian was overpowered enough to let him defeat Alan. Alan, in his turn, blew the genie away with one punch, and then dumped Alibaba into a volcano.
Emokis. A fat gorilla of a woman, and one of the strongest Bishops in Chess. She is some sort of unholy fusion of the evil queen from Snow White and Gretel. Her weapons are a magic sword who she bullies into calling her "the fairest in the land" instead of Snow, who she fights (when it finally does speak its mind, she destoys it), and a power-boosting Ärm called "Candy House". She eats the candy house in battle to increase her size and physical strength several times over while fighting Snow.