Royalty Super Power

There's a reason that the royal family is the one in control of the kingdom. Their bloodline is the one with the powers. Their line is associated with magic, or telepathy, or some other sort of supernatural ability.

Sometimes this is the product of Superpowerful Genetics, other times it's an object passed down, or a ritual that the royals invoke that grants them their powers. Other times it is just handwaved as the Divine Right of Kings with a deity granting them their abilities, or just because Every Thing Is Better With Princesses.

Subtrope of Supernatural Elite, supertrope of Fisher King. Compare to Authority Equals Asskicking. See also Hive Queen, God King, and Vampire Monarch.

Anime and Manga

 * Sailor Moon: Being a Magical Girl in the royal blood with everyone being princesses and passed down from mother to daughter.
 * Tenchi Muyo Tenchi is a member of the Juraian Royal Family. As such, he can operate Jurai's trees.

Comic Books

 * While all members of The Inhuman race have superpowers, those of their Royal Family tend to be the most powerful.
 * One issue of Justice Society of America reveals that Wildcat is descended from royalty, which gives him the power to defeat that story's villain in a Prophecy Twist.
 * The Superman vs Doomsday comic: Doomsday, an invincible regenerating monstrosity that adapts to anything attacking it to the point of Won't Work On Me, experiences his first defeat when the royal family of a planet commit mass suicide to merge into a being of Pure Energy (which Doomsday had not yet encountered, and so was powerless against it). Unfortunately, they cast his body into deep space instead of burning it... Said royal family had developed limited Psychic Powers through centuries of inbreeding, but it was only through their sacrifice that these powers could be unleashed.

Literature

 * In The Lord of the Rings the kings of Gondor have healing abilities.
 * Everyone in Xanth has a magical talent, but there's a legal requirement that the king must be a Magician (someone whose talent is particularly powerful). Over the course of the series, one family has kept the throne for several generations because they're descended from a character who was given the gift that all his descendants would have Magician-class talents.
 * Labyrinths of Echo explored the implications. The protagonist immigrated to a very rich kingdom. Later his boss explains the reason why here only scholars know what "drought" means: crown princes of several successive dynasties were initiated into a special magical tradition giving the ability to strike deals with the land itself and received Training from Hell just to be ready for fighting off endless attempts to manipulate or magically influence them - to the point that "he was a crown prince and trained accordingly" is given as a reason why a king-Arbiter managed to control his powers. In many generations of batshit insane mages almost no one tried to overthrow the monarchy or attack a specific king: the total amount of known conspiracies to this end was 24 over millenia-long history of several dynasties, 16 of them during the Troubled Times - protracted civil war of almost randomly allying and feuding magical Orders, when no one even gave much of a damn that one of these seriously tried to bring the end of the world and another to prevent the same, the sky changed every hour or so to colors of different orders whenever mages were in mood to show off without blowing up each other, and (as one participant later observed) no one in right mind would choose to stay in the capitol to begin with. Rebellious mages screamed for blood of the leader of the magical order allied with the crown and long after this mess ended avengers popped up once per tenday or so. But the King's main personal nemesis was his own master of ceremonies. In a land "full of two-bit clairvoyants" the monarch travels incognito with two guards and a token cover-up: lots of people could track him if they wanted, yet no one actually tries.
 * Only the nobles in The Familiar of Zero can use magic, and their children can use magic via Superpowerful Genetics. And in a special case, a user of Void Magic must be descended from the either one of the founding leaders of any of the four countries.
 * In The Dresden Files, being a descendant of royalty is one of the criteria for being a Knight of the Cross.
 * Both the House of Haldane (rulers of Gwynedd) and the House of Furstan (rulers of Torenth) in the Deryni works are deeply associated with magic.
 * The Haldanes ruled Gwynedd long before their powers were discovered; the discovery of the abilities facilitated the restoration of the dynasty to the monarchy after an interregnum of some eighty years. Subsequent Haldanes used their powers to help retain their throne in the face of their rivals' repeated efforts to retake the country.
 * The Furstans largely train to use their powers like other Deryni, but the monarch's investiture is a magical ritual involving the tomb of the dynasty's founder, which is depicted throbbing with arcane power. Kelson Haldane and some of his courtiers visit the tomb with the young King Liam and his uncle before the ceremony, and even Liam is noted as avoiding touching the tomb.
 * In Dune the Bene Gesserit manipulated marriages between members of certain houses for about ten thousand years in an attempt to breed a Kwisatz Haderach who could access both sides of his lineage's Genetic Memory and see the future perfectly. The end result was Paul Atreides, who used his powers to become the messiah of the Fremen of Arrakis and Emperor of the known universe. His son, the God-Emperor Leto II, inherited the same powers and spent the next four millennia selectively breeding his sister's bloodline (including repeated inbreeding with clones of Duncan Idaho) for the ability to not be viewed by prescience.
 * In A Song of Ice and Fire members of house Targaryen supposedly have the blood of dragons, though the only current one who is fireproof and can command the loyalty of dragons is Daenerys.
 * In Margaret Weis's Star of the Guardians series, the ubermensch ruling class have perfect genetics, psychic abilities, and the sanction of God.
 * In the Inheritance Trilogy the Arameri royal family has a variety of superpowers- they can command the Enefadeh (a group of powerful gods), and also command weaker members of the family depending on their sigil.
 * Members of the Rakan dynasty, rulers of the ancient Golden Anaxia in Reflections of Eterna, wielded magical powers connected to the very fabric of the world of Kertiana, but the knowledge of how to use them has been lost as the dynasty almost died out. Likewise, the four ducal houses of Golden Anaxia also wielded some sort of Elemental Powers but forgotten all or almost all about them.

Tabletop Games

 * The RPG 7th Sea has this.

Video Games

 * The emperor's line in Oblivion has dragon blood in them and can even turn into dragons.
 * Radiant Historia: Eruca, the princess, is the only one who can perform the ritual to delay Desertification.
 * Fire Emblem Jugdral has the various noble families of Crusader lineage. Their Holy Blood gives them significantly higher natural abilities than commoners possess (which takes the form of special stat boosts) but more importantly, only those of the right Crusader blood can use their family's respective holy weapon or spell, all of which are devastatingly powerful.

Web Comics

 * In The Cyantian Chronicles, until a recent coup, the three highest ranking castes in the Fox Empire were genetic elites with enhanced strength and regenerative abilities. The Blacks also had the ability to project energy blasts.