Ah, The Sun. The celestial object around which our world turns. A ball in the sky that brings light to darkness, life to plants, and warmth to all. It's also, of course, a giant nuclear furnace more than three hundred thousand times the mass of our puny little planet that burns more than four million tons of hydrogen into energy every second, the biggest source of energy for four light-years in any direction, so it's understandable that one might want to harness or replicate that kind of power.
See, sometimes, the power of the sun itself is classified as a sort of Elemental Power. The effects of sun-power are many and varied: you could shoot ultraviolet rays to give people nasty sunburns, perhaps channel a beam of light to fry a vampire, maybe heal people with the mystic power of sunlight — somehow. And of course, you could always just go straight to the nuclear fusion. Atomic fire is always a nice way to make sure your target is dead, and it's much easier to Hurl It into the Sun if you can make a little mini-sun.
The power of the sun is a lot like a fun little cocktail of Playing with Fire and Light 'em Up, with an occasional side of nuclear weapons. If elements oppose each other, the power of the sun will generally be opposite Lunacy.
If a device is simply powered by solar panels, photosynthesis, or even by a Dyson Sphere, it doesn't quite count as this trope: it generally has to utilize sunlight, or solar rays, or nuclear fusion to qualify as the power of the sun.
There's also the Meteonite from Best Wishes. Though the episodes are still postponed at the time, trailers and promotional material for the "Team Rocket vs Team Plasma" two-parter show that the Meteonite is solar powered, and it can be made into an artificial sun that shines even at night. Its' rays put pokemon under it's control, which is why Giovanni wants to harness its' power. At the climax of the story it apparently becomes a sun, as shown here at 1:29.
In Digimon Adventure WarGreymon's most powerful attack consists in throwing a sun. He even has the image of a sun on his wings, although he's officially a fire-elemental. Wizardmon is also thought to have sun-powers.
The Marvel Universe has a number of sun-using heroes: the original Sunfire (this one's also a villain though), his sister Sunpyre, and the Exiles' Sunfire. As well as Sunspot, who in his current incarnation can absorb sunlight and release concussive blasts of solar energy, with a considerable heat and light projection component.
The Sentry has "the power of a million exploding suns."
Most of Stark's Iron Man armors have a solar energy collection function that can keep them working on a basic level, but that's mainly an emergency backup that cannot seriously provide enough power fast enough for combat.
The Green Lantern villain Evil Star wields the Starband, which fuels itself on the light of the stars and gives him incredible powers. Interestingly, when he tried to fight Superman, he only made Superman stronger. Superman explained that starlight is the same as sunlight, his power source.
Lucifer in his Vertigo incarnation is the Morningstar, the light of God, responsible for shaping and lighting the stars through his will alone. He is able to channel this power whenever he likes it, with fiery and usually instantly-fatal results.
The Big Bad in Die Another Day uses a Kill Sat that reflects and focuses sunlight into a single destructive beam that can be targetted anywhere. Of course, it can also be used for beneficial purposes, such as providing warmth, which it does exactly once.
Megamind: Megamind's latest scheme involves using the power of the sun to kill Metroman. It takes a long time to warm up...
Dr. Octavius' device in Spider-Man 2 was meant to create "the power of the sun in the palm of my hand." Specifically, a controlled nuclear fusion reactor. Which, admittedly, would be extremely revolutionary. He achieves, except for the "controlled" part, as the "mini-sun" has one hell of a magnetic field.
And everyone (in-universe) seems to completely overlook the fact that he already invented and nearly perfected cybernetic limbs and true AI just to help him handle the complex manipulations of the controls for his fusion project.
Seemingly half the point of Sunshine is to demonstrate the incredible radiant power of the sun. Everyone's lives both depend on and are threatened by the sun during the movie, and while the Sun is dying, it is still incredibly powerful.
Superman IV: The Quest for Peace has an evil Superman clone that has powers derived from the Sun as well. Thing is, appearently he "turns off" when not exposed to sunlight - and, naturally, there's no consistency on this on the movie.
Slaver Sunflowers in Larry Niven's Known Space setting. When in groups, they can collect and concentrate sunlight on a specific target, incinerating it.
Short story "Sign Among The Stars" (1958). A sun furnace (a pair of giant mirrors) can concentrate sunlight and use it as a beam weapon.
A short story that appeared in an old Analog magazine (can't find it). Someone programmed all of the movable mirrored windows in a large building to be at just the right angle to reflect all of the sunlight hitting the building into a specific room in a nearby building, murdering the person inside.
Wicked Lovely has the summer court, who use sunlight as a tangible elemental ability, the same as the dark court's shadows, the winter court's frost, Sorcha and Bananach's warping reality, and Olivia's stars.
Robin McKinley 's Sunshine features a protagonist who draws her magic from exposure to sunlight, and whose health actually deteriorates without said exposure, in what may be the ultimate case of seasonal affective disorder. Appropriately enough, she uses said power to get involved in a war against vampires.
The starship Destiny in Stargate Universe was designed to travel across multiple galaxies without a crew for an extended period of time. By the start of the series, it has traveled across billions of light years. How did it find the power to drive its engines across such massive distances? By diving into stars and scooping up solar matter, of course.
In Smallville Clark et al. figure out the connection his powers have to the sun when a major solar storm causes them to intermittently stop and start working, resulting in no end of havoc.
Many religions have one or more solar deity/ies, but how powerful they were tends to vary depending on how the religion. Helios from the Greek Mythology had to ask Zeus to punish the people who ate his sacred cattlenote How powerful he is tends to vary, however, as while he is depicted as ridiculously weak at times, he is also depicted as a violent and even outright destructive force in at least two seperate occasions. Amaterasu from Japanese Mythology is ruler of the gods, but powerless against her brother the storm-god Susannoo. Exceptions include Neto, who was both a solar deity and a deity of war, and appearently a very powerful one at that. Ra or Horus are powerful gods with the former being a creator-deity and the latter vanquishing the god of storms and chaos. Huitzilopochtli from Aztec Mythology was a god of sun and war and one of the most powerful deities. There's also Haemosu from Korean Mythology, Heavenly Emperor's son and a very powerful god(beating god of the river in a shapeshifting duel), and founder of the Buyeo and Goguryeo Kingdoms.
Some systems had both a sun god and a personification of the Sun. For instance, in Greek mythology, Apollo was the "god of light" (effectively a solar deity), while Helios was the Sun itself.
Sometimes, the Sun is the eye of the ruling god. Helios, for example, is often reffered as the eye of Zeus, Odin's remaning eye is sometimes described as the Sun, et cetera.
In abrahamic theology Shamsiel is usually said to be the angel of the Sun. In Paradise Lost, though, it is Uriel who wields this power.
Archangel Michael is also frequently considered the planetary angel of the Sun. Curiously, he and Shamsiel share multiple traits, such as being cherubs, guardian the Fourth Heaven and the Garden of Eden.
In Gnosticism, the Sun is represented by the Archon Adonaios, though some sources list Iao instead (which otherwise stands for Jupiter). In a twist, however, since the Sun is an Archon, which work for Yaldabaoth, it is at best an hostile power.
Dungeons & Dragons. In the 2nd Edition Al-Qadim setting: there are a few sun-powered spells: Sun Stone (a stone held in sunlight becomes an incendiary missile), Sundazzle (sunlight causes blindness), Sunfire (solar-powered Fireball), Sunwarp (powerful, though limited mirage-based variant of Mirror Image)
Some or other Sun deity is almost obligatory in any setting and the priesthood of each, of course, has sun-related spells and powers.
For example in 3.5, clerics of the sun god Pelor can take the Sun domain. Which, in addition to giving them many heat and light-based spells, including the extremely powerful Sunburst, which lights up everything within 10 feet of the cleric, allows them to perform a "greater turn undead", which focuses powerful sunlight instead of positive energy. Instead of merely scaring undead away, a Greater Turning turns them to dust on the spot.
Sun Mages in Spelljammer campaign Astromundi Cluster. The Antilan Empire wizards purchased the secrets of sunmagic from the Arcane and kept as a secret weapon.
"Sun" (Radiance) quasi-elemental priests in Dark Sun. Though they are messed up unlike the rest of the bunch, without a good explanation.
There are also spirits from the Shadow which are basically sun elementals. These are noted as bearing a passing resemblence to fire elementals, but appear more transcendent and powerful (they're among the most powerful spirits in the Shadow) and also have a theme of bringing "illumination". They also attack darkness spirits (which are conceptual rather than elemental), and have a relationship with werewolves (children of Luna) that ranges from "grudge" to "attack on sight."
For a somewhat darker twist, there's the sorcery spell Total Annihilation, which draws on the destructive potential of a different sun — Ligier, the ever-burning green sun of Hell. It's pretty much a fantasy nuke.
The sun god himself, the Unconquered Sun, is generally invincible, but in the latest edition the Scarlet Empress turns Bitch Queen of Hell and schemes a way to kill him by blotting out the skies, and effectively bring about Armageddon to the land. It's pretty epic.
Warhammer has Solkan, one of the gods of order, which is a solar deity that may offer his followers fire and light powers. Like all the gods of order, he doesn't show up very much (except for some refferences in the novels); considering how he is, that may be a good thing.
It also has the mages of the White College of Magic, who specialise in truth, philosophy, healing, and using the blinding light of the sun to burn daemons.
Magic: The Gathering puts sunlight in the white part of the color-pie. Shown to devastating effect in cards such as Wrath of God.
In Bayonetta, the Lumen Sages had the Sun as the source of their powers (as opposed to the Umbra Witches' own Lunacy and Demon Summoning); Father Balder, the last of these sages, even has solar motifs in his battle mode, with his clothes turning blue/yellow (the main wavelengths of sunlight), and his peacock feather like wings vaguely resembling sun rays.
In the Boktai games, the protagonist Django uses the "Gun Del Sol", a solar-powered gun that shoots sunlight (and later a solar-powered gauntlet called the Sol de Vice, which gave melee weapons similar powers). Very useful for a vampire-hunter. What was especially interesting was that the game had you power the gun using real-life sunlight. A UV sensor on the game cart made sunlight shine into the game world when it detected sunlight.
The Gun Del Sol is also a weapon (in this case, a chip) in the Mega Man Battle Network series. True to form, it's more effective when jacked-in to an outdoor location.
In Pokémon, there is the move Solarbeam: a powerful grass-type move that has the user charge up sunlight for a round, and then fire a beam of pure solar energy at the foe. There is also Sunny Day, which generates intense sunlight for 5 turns. During that time, Fire moves are empowered, Water moves are weakened, and Solarbeam's charge-turn is eliminated, making "Sunnybeamers", Pokémon with Sunny Day and Solarbeam, extremely powerful, especially if they also know fire moves. The move Weather Ball changes its typing and becomes twice as strong during abnormal weather: it becomes a Fire-type move during intense sun. Finally, there is the move Morning Sun, which restores a Pokémon's health. How much is restored is dependent on the weather, and it heals the most during a sunny day.
Some Pokémon Abilities are dependent on the sun. Chlorophyll doubles a Pokémon's speed during intense sunlight, and Solar Power makes them stronger in sunlight but also hurts them. Meanwhile, Castform has the Forecast ability, which changes its form in weather: in intense sun, it becomes a Fire-type that looks like a sun. Cherrim has the Flower Gift ability that boosts several stats during sunlight. It also changes shape, but not type.
Although fairly subtle, Ho-oh and it's unique abilities (the attack "Sacred Fire" and being able to resurrect the dead) are based on this. This becomes more obvious when it is paired with Lugia, the Solar and Lunar dichotomy becoming more apparent.
Some other Pokemon have associations with the sun: there's Larvesta/Volcarona, Espeon (which even has a Lunacy counterpart in Umbreon) and Groudon (it's more associated with land and continents, but it has the ability Drought which causes permanent sunny weather).
In Final Fantasy Tactics A2, the Geomancer spell Shining Flare generates an intense burst of sunlight for fire damage. It can only be used when the weather is sunny.
Additionally, the illusionist spell prominence claims to use the fires of the sun.
While not explicitly coming from the sun, the Flare spell in many Final Fantasy games is described as generating a nuclear fusion reaction. This leads to variants like Flare Star, which at least looks more like a sun going nova in the party's face, and the rename of Bahamut's signature Mega Flare attack in Final Fantasy VI's SNES translation: Sun Flare.
In Final Fantasy VII, Sephiroth's flashiest attack is Supernova, where he attacks the party by blowing up a (our) sun at the party. Funny thing: he can use it multiple times and it cannot kill the party.
Three different characters in the Touhou Project have been seen using solar power:
Patchouli Knowledge has Sun as one of her seven elements (alongside Fire, Water, Earth, Metal, Wood, and Moon). Spells with this element include Royal Flare (alone), Hydrogenous Prominence (Sun and Water), Photosynthesis (Sun and Wood), and Royal Diamond Ring (Sun and Moon).
Utsuho Reiuji, on the other hand, swallowed the corpse of a sun-god, giving her the power of nuclear fusion. This manifests in, among other things, gigantic nuke-bullets, attacks based off of suns, stars and various constellations, and the ability to create artificial suns. She was led to get that power so that she could be used to build and maintain a nuclear power plant running off of suns made from her nuclear fusion.
Sunny Milk, the fairy of sunlight, uses the sun to strengthen her abilities. She is also capable of optical camo by refracting light.
In Mega Man 10, one of the robot masters is Solar Man, from whom Mega Man acquires the Solar Blaze weapon.
In Mega Man 4, Pharaoh Man's Pharaoh Shot draws upon the power of the sun, and when Mega Man learns the attack, it generates a miniature sun above him when he charges it up.
In Chrono Trigger, the power of the sun was the major power source of the Kingdom of Zeal. Eventually though, the seemingly limitless power of the Sun Stone, which stored the solar energy, was all used up, and they turned to the power of Lavos. That didn't turn out too well. The player is able to take the now-powerless "Moon Stone" and place it in a patch of sunlight (on an island that for some reason never changes its position for millions of years or is affected by an apocalypse) and retrieve it in the future, where it has finally absorbed enough sunlight to be used to create Lucca's strongest weapon and a very powerful accessory.
The Sun Rune, along with both Dawn and Twilight Rune from Suikoden V. Apparently, the influence of the Sun Rune is so powerful to the point it can corrupt its wielder. If you gather all of the 108 Stars of Destiny, it will move to its nurturing phase and brings back Lyon to life.
Ōkami well, Amaterasu is the Goddess of the Sun, so it does make sense.
Helios in God of War, being the god of the sun. He even shouts it before blinding Kratos with intense sunlight from his head.
NPC Saber from Fate/EXTRA who is actually Gawain uses Excalibur Galatine, Excalibur's sister sword, which 'glows with heat rays of the sun'. He also is immune to your attacks as long as the sun is shining which is usually all the time during the tournament.
In World of Warcraft: Cataclysm, the tauren founded the Sunwalkers, a group of paladins and priests who revere the sun (or An'she, the right eye of the Earth Mother) as their idol and patron, which is a direct balance to the druids who use the power of the moon. Whether this is really the power of the sun at all is up for debate, as the Light is a universal force fueled by strength of will regardless of whether an individual personally acknowledges it, but depictions of Sunwalkers outside the game seem more in line with priests and paladins of other races than with other sun-based beings.
Balance druids seem to have followed in the footsteps of the tauren (since many of them are tauren themselves) and their Balance specialization has shifted somewhat away from raw natural energy and plants towards a motif of celestial bodies. In addition to the power of the moon that they've always had, supplied by the night elves' moon goddess Elune, they've also added solar power to their repertoire (notably, manifesting differently than the Sunwalkers) and their abilities revolve around periodically shifting between the two powers.
Rajh, final boss of the Halls of Origination, is the Construct of the Sun and uses several sun-based abilities, such as Solar Winds.
The entire culture of the high/blood elves runs on the sun. They draw their power from the Sunwell, a font of magical energies, their city is coated in warm color and sun references, and at least half of their greetings involve the sun somehow. This is a direct contrast to their cousins, the night elves who have a similar reverence for the moon, though the night elves treat the moon as an object of worship, while the high/blood elves see it more as a symbol of their rejection of everything the night elves are. It's a common misconception that the high/blood elves worship a sun god, but that's just not true.
Cosmology, a school of magic in Romancing Saga consists of spells which use the Sun's power to heal allies or cause damage to enemies.
Fallout 2 has a secret weapon called the Solar Scorcher, found only in a random encounter. It's fueled by sunlight, and so is incredibly powerful in daylight, but next to useless inside caves/buildings or at night.
Mouri Motonari from Sengoku Basara worships the sun and can use its power to drain the enemy's health. He just won't shut up about it.
In Shadow Hearts: From the New World, Shania's final Fusion is Tirawa, the Spirit of the Sun. Its ultimate move is "Sun Flare", which causes the sun to hurl fireballs at her enemies. In-story, the Spirit has the power to burn away any and all evil which you need to do just that by maxing out Tirawa's statues in order to get the Good Ending.
Florence uses a sunrise to demonstrate to Helix the safety of a fusion reactor, calling it the largest reactor in the star system.
Phaeton has solar and lunar celestial affinities, Solar phaetonians can use pure sunlight to channel some powerful beams, lunars can use sunlight reflected off celestial bodies to do the same thing but inverted. Just don't let the beams touch at equal power.
In Worm, Sundancer can create and move a miniature sun and dial it up to such extreme temperatures that it pretty much instantly incinerates anything that isn't absolutely invulnerable.
In The Venture Bros., there is the troubled superhero Captain Sunshine. His superpowers are solar-powered and involve firing high-energy "Sunbeams" that cause painful sunburns at least.
Hanna-Barbera's Birdman, who also needed sunlight to recharge his powers. He could fire "solar rays" from his fists and create a "solar shield" to protect himself.
In Harvey Birdman, Attorney at Law it is noted that he does still get his energy from the sun, which becomes a problem when he develops skin cancer and can't be out in the sun (and subsequently becomes addicted to tanning cremé). Thanks to Snap Back, this is forgotten in a later episode where it's mentioned again that he's solar powered, and he complains that it's 'lame' compared to those that got their powers from radiation or coal. And in the final episode he has to utilize his solar powers when he returns to being a superhero to stop Nitron.
In The Secret Saturdays, Drew has a Flaming Sword that is powered by the light of the sun. It also has a blue setting that is powered by moonlight, which is, after all, reflected sunlight.
In the My Little Pony 'n Friends episode "The End of Flutter Valley," we learn that Flutter Valley is kept perpetually green thanks to the power of the Sunstone, which appparently amplifies the sun's rays. When the Sunstone is stolen by the bees of Bumbleland, Flutter Valley starts to wither away. Newly situated in Bumbleland, the stone at first turns it from a frozen wasteland into a beautiful forest, but after a few hours the rays become too powerful and the forest starts to burn.
In My Little Pony: Friendship Is Magic we have Princess Celestia, (co-)ruler of Equestria with the power to raise and lower the sun (and while her sister is... away, the moon as well). It's not altogether clear how much of her power is in turn actually derived from the sun and how much of it is "just" her own innate alicorn magic; in either case moving the literal celestial body is in and of itself no mean feat.
In Avatar: The Last Airbender, Firebending is ultimately this, and even the corrupted form of Firebending is tied to the sun. While firebending still works at night, it is much weaker at that time. During a solar eclipse, even the most powerful firebenders are unable to conjure more than a spark.
Zuko later states during his and Aang's travels to the lost Sun Warrior civilization that the primal form of Firebending, as taught by the dragons, is 'like the sun, but inside you!'. Notably, he becomes vastly more powerful after this fieldtrip, implying that Firebending is pretty much this trope straight.
Aqua Teen Hunger Force: When Master Shake steals Frylock's magic jewel he proclaims that "[He] has the power of a thousand suns"
Aladdin: The Series: The Ancient Shamash is a magical orb with this power from the episode "The Lost City of the Sun".
Plants with their photosynthesis.
You, yes you, draw vitamin D and warmth from the sun.
This is zig zagged because, while the sun does give you vitamin D and warmth, it can also give you skin cancer and really painful and itchy sunburns when you get too much of it.
Zig zagged, yet again, with many types of plants can get dried out when exposed to too much sunlight.
Completely inverted with some types of plants and fish who need little to no sunlight at all, some even hate the sun.
Solar furnaces use mirrors to focus sunlight to a point. The temperature at the point can reach over 2000 degrees celsius
Due to poor design, a hotel in London is melting cars parked near it.