Related to Lunacy and The Power of the Sun, Star Power is magic fueled by, of course, the stars.
Generally comes in one of two forms, "Classical" and "Lovecraftian". "Classical" star power, derived from the traditional use of the stars and the motions of the planets to predict the future, is concerned primarily with fate and divination. "Lovecraftian" star power takes its cues from H.P. Lovecraft (of course) and evokes the unfathomable otherness and distance of the stars and whatever inhabitants they may have.
Causing meteors to fall from the sky to strike your opponents is not out of the question for either type. On the opposite side of the scale, this may extend itself to power that comes from galaxies or even the entire frakken universe.
Often the reasoning behind using something made of Thunderbolt Iron. If the person who uses Star Power is actually made of stars, see Celestial Body.
For related "space" powers, see Gravity Master and Reality Warper. Not to be confused with the webcomic Star Power or that other Star Power.
Saint Seiya is built on this early on, with both heroes and villains taking their powers from a constellation (From Pegasus Seiya to Gemini Saga). Later enemies had other sources for their powers, though.
In Cardcaptor Sakura, the whole second series was about her having to transfer the Clow Cards from their old energy source (The Sun and the Moon, which her predecessor used) over to her power source - the power of her star.
Pamoon, one of the Millennium Mamodos from Zatch Bell!, has spells revolved around this.
In the manga version of Yu-Gi-Oh! GX, Kaiser's monsters are all named after stars, specifically those of the constellation Draco.
In Yu-Gi-Oh! ZEXAL, every known resident of the Barian World is loosely named after one of the stars of the Big Dipper: Durbe after Dubhe, Alit after Alioth, Misael after Mizar, Gilag after Merak and Vector after Phecda.
Nanoha Takamachi from Magical Girl Lyrical Nanoha has two themes: Stars and a Feather Motif. To perform her Starlight Breaker, she gathers the residual energy left by magical attacks in a battlefield in form of thousands of starlights. Other characters who know Breaker magic are Reinforce Eins, who copied it from Nanoha, Teana Lanster, who learned it from Nanoha, and Miura Rinaldi, who also has a star themed Intelligent Device with the name Star Saber. In Miura's case, her attacks are mostly close-ranged based and her two most powerful attacks have the names Bakken: Seiōha ("Sword-draw: Starbright Blade") and Bakken: Tenshō Seiōha ("Sword-draw: Heaven-piercing Starbright Blade").
The DCU has had several characters powered by the stars, in about the same way Superman is powered by the Sun: Starman (in the golden age), Hawkman (at some period in silver/bronze age), and Dr. Regulus (LSH villain).
In The Silmarillion, this was the domain of Valar Varda, the lady of stars. Afterwards, the elves became always associated and very fond of starlight ("Eldar" more or less means "of the stars" in Quenya), though sadly few show such magic.
Live Action TV
In Kamen Rider Fourze, both heroes and villains are powered by cosmic energy, but the villainous Zodiarts fit best because they're themed after constellations.
And conceptually at least, the Master of the Starry Night paragon path from the Arcane Power supplement is all about cutting out the eldritch abomination middleman in favor of discovering and harnessing the presumably more natural power of the stars themselves.
In the Greyhawk setting, Celestian is the deity of space and the stars. He has a number of space/star related powers, including Aurora Borealis, Comet, Meteors, Space Chill, and Starshine.
One of the eight magic schools in Warhammer is the Lore of Heavens, or Astromancy; it's mostly the Classical (fate manipulation and divination plus meteors) type, but with added aeromantic and lightning-based spells for combat.
The Sidereal Exalted get a variant on this, especially in the form of Astrology, where they can weave alternate fates that grant them benefits to certain tasks based on the constellation they're using.
In the Yu-Gi-Oh! game the members of Sacred/Constellar archetype are named after stars, clusters of stars, or in a few cases, whole galaxies. Most of them are named after stars in the constellations of the Western Zodiac.
Pathfinder sorcerers can choose Starsoul as a bloodline, which means their inherent magical powers come from some hereditary link to the stars and the empty void. They get space-oriented bonus spells and even eventually develop physiological changes, such as immunity to cold or no longer needing to breathe, to let them survive in the void of space.
Star Ocean: The Second Story, among its overload of elements, had "Star" as distinct from both "Light" and "Vacuum" (which itself was distinct from "Void"). Most of the Star-elemental spells were cast by Celine. When the PSP version greatly simplified the element system, Star-elemental spells were merged into Light.
In Touhou, Marisa Kirisame uses spells themed around stars (and to a lesser extent, galaxies, comets, and so on). Likewise for Mima (who is widely assumed to be Marisa's teacher). And the fairy Star Sapphire is literally powered by starlight, as well as having a star-based spellcard theme.
Disgaea has "star magic" and mages as its most powerful offensive spell element.
Otani Yoshitsugu from Sengoku Basara is astrology-obsessed (his title is "Sky Watcher") and believes in a red comet that is a harbinger of human misery and that he will invoke it. All his powers are astrology-themed, named after constellations, stars, planets, or mythological beings associated with stars.