The anime Darker than Black fits this rather neatly, having a mysterious event which opened two mystical singularities known as "Heaven's Gate" and "Hell's Gate" — in South America and Tokyo, respectively — resulting in people from around the world being transformed into either Contractors (those with special powers who are stripped of their emotions/morality although, that turns out to be much more complicated) or Dolls (people left almost completely non-sapient who are used as living tracking devices), and the atmosphere around the earth being replaced by an Alien Sky that cut off Earth from the rest of the universe.
NEEDLESS has a WWIII level event causing a 'black spot'. Many of the people within this area have superhuman powers. Late in the anime, it's revealed that originally there existed a Crystal Dragon Jesus Figure existed previously within the area and his death caused the powers to spread throughout the black spot.
Calumon from Digimon Tamers is something of a sentient version of this. It's hinted throughout the series that he's the power of digivolution incarnate, with reactions and shows of power from him whenever the Tamers' digimon needed to evolve. Calumon is then captured by one of the Digimon Sovereign, and after being rescued and his captor beat around by one of his peers (as well as the Tamers), he fully 'awakens' and summons an army of Digimon to warp them all to Mega-level in order to fight the D-Reaper.
In the Tiger & Bunny universe, people started developing or being born with many and varied superpowers about forty-five years before the time the show's set in. No one is quite sure why this happened — they just roll with it.
The X-Men have the detonation of the Atom Bomb as the cause for the explosion in their birth rates, having been a very tiny percentage of the human population beforehand. They ain't called "The Children Of The Atom" for nothing.
In Malibu Comics' The Ultraverse, the only sources of superhuman powers were magic, technology ("wetware") or "the Jump Start" — an alien artifact located on the moon that every so often sent out bursts of energy that granted humans superpowers, at first theorized to be intended to advance humanity to the point where we could reach the moon and free it, but later revealed as attempts to gather its scattered components including the Nanomachines that had long ago infected all life on Earth including humans.
In another of his comics, Supreme Power, all superpowers (except Hyperion and Zarda's) were caused by a nanovirus that came to Earth along with Hyperion.
The setting of Earth X comes from this, but the reason is not revealed until later in the story. It turns out that it was Black Bolt, who used a weapon to cast Terrigen Mists down to Earth so that the Inhumans would not be seen as outcasts when they left Attilan. What he apparently didn't predict is for Earth to turn into such a Crapsack World.
The Elementals comic by Bill Willingham had the Shadowspear, a mass of supernatural energy collected by Big Bad Saker to help him conquer the world; when Saker is defeated by the Elementals, the Shadowspear spell runs wild and becomes attracted to pain and death, causing various people and animals all over the world who have died in especially weird ways to be resurrected as supernatural beings, most of whom fought the Elementals.
What's more, an extremist religious group learns how the Shadowspear works and sacrifices hundreds of its followers in gruesome ways, trying to create their own superhumans. And it worked. The vast majority of these "martyrs" died, but enough were empowered to create the Rapture super-team.
In The End League, most superpowers are a result of the Green Event, wherein SupermanAstonishman was tricked by Lex LuthorDead Lexington into blowing up a crashed alien spaceship, releasing exotic radiation from the ship's power core. The radiation killed around 3 billion people but empowered several hundred thousand.
Wildstorm Universe had several - the Comet Effect, Gen Factor, being a partially human from one of the alien races that masquaraded their way through Earth's history, whatever it was that created Century Babies, exposure to the Snowflake... that should about cover it.
In Project Superpowers Pandora's Urn didn't so much mass-empower the heroes as it twisted their existing powers and/or skills in bizarre ways.
Transformers: Generation 2: Redux (otherwise known as the comic book that was distributed at BotCon 2010) revolved around the Decepticons experimenting with forestonite. Eventually, an attempt to destroy it to keep it out of the Autobots' hands results instead in forestonite gas granting superpowers to all the Transformers present (along with the occasional new look).
In the Ultimate Marvel universe, mutants appeared in the world thanks to Super Soldier experiments performed on Wolverine, the first true mutant.
Minor but awesome example: when the young Matt Murdock saved an old man of being run over by a truck, a tube of mysterious chemical ooze from said truck hit his eyes, granting him Super Senses. That same tube of ooze fell then into the gutters, covering four turtles and a rat. Yes. No, I'm not kidding. This means that the same Freak Lab Accident created six superheroes.
Seven including Jessica Jones, aka Jewel. Her family was riding in a car which collided with the truck carrying the chemical. The rest of her family was killed, she got powers.
Most of the initial heroes and villains in the Dakota Universe got their powers from "the Big Bang," when police tried to douse the participants of a massive multi-gang rumble with an experimental radioactive tracker. Good job, men!
Captain Carrot and each original member of his amazing Zoo Crew gain their powers because of exposure to fragments from the same strange meteor.
Downplayed in Strontium Dog: Most characters in the series who have some form of superpowers got them due to Strontium-90 fallout from the Great War, but vanishingly few of those exposed to Strontium-90 came out physically or mentally superior to baseline humans.
DC Nation, in their version of Blackest Night, had hundreds of rings in every color of the emotional spectrum descend on Earth for the final fight. This included black ones.
The Nucleus Incident, a very popular Team Fortress 2 fanfic, involves the RED team being exposed to a blinding light the glowing machine in the center of the Nucleus map gives off one day. Each team member wakes up some time later to find out they've acquired strange superpowers and the BLU team have superpowers of their own.
In Poké Wars, Ho-oh uses the orb of creation to substantially boost the power of Pokémon attacks and make them lethal. In addition, Lugia uses his own orb of creation to remove the dampeners of humans, granting them the ability to perform superhuman physical feats.
My Little Avengers has three: the first happened in the distant past, when Asgard was destroyed, and the magic released by it created Celestia and Luna, as well as the first Unicorns and Pegasi. The second occurs when Celestia is forced to release most of her own magic when Loki attacks her; this causes random mutations across Equestria. The third occurs at the end of the story, when Loki dies, and his magic is released in the same way. According to him, this will insure that everypony (and every other species) will all be mutants within a few generations.
Downplayed in A Posse Ad Esse, a Die Anstalt fanfic in which the six playable toys get specialized superpowers. The energy wave coming out from Dr Wood only affects the toys inside the asylum at the time; in fact, not even that far, since Dub is found without any, being "furthest away from the blast".
The entire plot of the Detective Conan fanfic Midnight White starts with a mysterious stranger breaking into a science museum during a Kaito KID heist and setting off a device that produces a strange blue/white smoke when caught. The rest of the plot revolves around the main characters and a few O Cs discovering and dealing with their powers and relationships, while trying to figure out what the mysterious stranger wanted.
Red Lightning has the Storm, which gave a significant minority in Peach Creek super powers.
In Fantastic Four movie, the cosmic storm served as the Mass Super Empowering Event for The Four and Von Doom
The Wild Cards book series has an alien virus that grants superpowers to about 1% of victims, while the other 99% either die horribly or become grotesque mutants. In 1946 it is released in the atmosphere over Manhattan, killing thousands and creating a few dozen supers. It's later revealed that a percentage of the seemingly uninfected are carriers when the virus manifests in their offspring.
In Philip Jose Farmer's "biographies" of Tarzan and Doc Savage (and the Massively Multiplayer Crossover "Wold Newton Universe" based on Phillip's stories), the Event is the titular Wold Newton meteorite. The radiation of the meteorite affected the passengers of a passing coach (and several animals in the area); their descendants were endowed with unusual strength, intelligence, and ambition, becoming the inspiration for many of the heroes and villains of fiction. (See the other wiki for more details.
Midnight's Children by Salman Rushdie has 1001 children born at midnight on the day India gained its independence acquiring low-level superpowers and a telepathic network as a result.
In Scorpion Shards, the protagonists' superpowers are triggered by the supernova of a distant star. The shards of the star's soul enter the bodies of all six of the infants born at the exact moment of its destruction.
At the end of the series, billions of stars go supernova simultaneously, transforming the entire next generation of humanity into Star Shards in recognition of the Shards showing mercy on their enemies in the final battle.
In The Grimnoir Chronicles books, at some point before the American Civil War, people all over the world suddenly started gaining superpowers.
In Wearing the Cape, the Event changes the world as we know it. For 3.2 seconds everyone in the world experiences complete sensory deprivation, along with a worldwide power outage. Since the Event, a small percentage of people who experience great trauma or stress become "breakthroughs," manifesting superhuman powers. The cause of the Event and source of these powers is never explained.
Perry Rhodan explains the sudden turn up of mutants with radioactivity because of the A-Bomb.
In the Mistborn books, the only way for a potential Allomancer of any kind to unlock their abilities is to face a near-death experience, resulting in an event called "Snapping." Late in second book and all through the third one, the mist sickness is a deliberate attempt by Preservation to forcibly unlock the Allomancy inherent in the entire human population by deliberately push anyone who has inherent Allomantic powers to near-death.
Live Action TV
The eclipse in Heroes at least looked like one of these at first, but it's not completely clear. The eclipse didn't grant everyone's powers, certainly not all at once, but it did remove everybody's powers once.
The cast of Misfits and most of the Monsters Of The Week are empowered by a mysterious storm that included misshapen black clouds and hailstones the size of dogs. Anyone struck by lightning got superpowers.
The series has arguably had three Mass Super-Empowering Events, the first being the infusion of the initial 4400 returnees with promicin. Many non-returnees later get powers when Well-Intentioned Extremists make promicin shots available to the public. The series ends with thousands of people in Seattle, including almost all of the remaining protagonists, getting powers as a result of the Power Incontinence of a character with the ability to release promicin into the atmosphere.
Buffy the Vampire Slayerends with a mass superempowering event, with Willow using the power of the Slayer Scythe to make all the Potential Slayers around the world into full Slayers.
The Hellstorm in GURPS Technomancer, which generated a wave of magical radiation which imbued magical abilities in hundreds of thousands of people in the fallout zone.
In the Pulp Action game Adventure!, which is a prequel to Aberrant, the Hammersmith Incident released waves of "telluric energy" across the globe, allowing for the appearance of low powered individuals to appear (and laying the seeds for the later explosion of Novas).
Godlike, a supers Tabletop RPG set in World War II, posits the appearance of superpowered "Talents" starting in 1936. Talents may believe they got their powers from magical artifacts or radioactive spiders or alien rays, but all are psychics with the power to warp reality to their will. Because they all share the same origin, all Talents can detect other Talent powers in use, and can attempt to interfere with other Talents in a contest of wills.
The 3.5 Expanded Psionics Handbook suggested a number of possible ways to Retcon in psionics; this was one of them, although not necessarily the Far Realm specifically.
In the Forgotten Realms campaign setting a battle between two deities resulted in the genesis of magic in that world.
Champions The New Millenium had the Wildstrike, in which millions of people around the world developed superpowers at once. In a subversion, these powers often came with horrific drawbacks or were very weak.
Exalted has a variation: the titular Exalted have always been a part of the setting, but after the breaking of the Jade Prison, Solars began reappearing in numbers unheard of since the Usurpation, and the brand-new Abyssal and Infernal Exalted showed up as well.
Also expressed in the origins of the Exalted, as the Exaltations were created by the gods to imbue their chosen mortal champions with the power to defeat the Primordials. They might have different flavors, but all have the same original reason for existing.
At least until 3e: the Liminals didn't show up until the Shogunate, and the Exigents are created on a case-by-case basis - some may well be results of the Primordial War, but others are created afterwards (e.g., the example Chosen of Harvests is a present-day creation).
In the Freedom Force games, when Mentor's ship is destroyed in Earth's orbit by Lord Dominion's forces, his supply of Energy X (the most powerful substance in the universe!), rains down all over Earth, empowering many heroes and villains.
In Vagrant Story, simply being within the city of Lea Monde begins to gift you with magical powers and extra senses. The same goes for your enemies, and even the Damsel in Distress, who gains the ability to see the hidden thoughts of the guys capturing her. The extra-sensory perception comes in handy for Ashley Riot to see cutscenes involving the villains when the villains are nowhere near him.
Lionheart: Legacy of the Crusader had a cataclysmic magical explosion known as the Disjunction during the crusades. Many people were possessed by spirits this time which granted them magical powers, though such possessed people are shunned and distrusted by normals.
City of Heroes has a grand total of three Events, two playing it straight and one inverting. The first is Marcus Cole and Stefan Richter drinking from the Well Of Furies, which supposedly opened the Pandora's Box on superpowers of all origins. Similar to the X-Men example above, mutants began appearing with more frequency after the first atom bomb was detonated. Finally, the Event was inverted at the beginning of the comics series when Lord Recluse (alias Stefan Richter) depowered all of Paragon City's extremely numerous heroes. Tying into this is the Event that re-powered all the heroes, the unleashing of Prometheus's Flame.
In Mass Effect, an explosion at a Singapore spaceport in 2150 caused Element Zero to be spread across a wide area, affecting many unborn humans exposed to it. If you were lucky, nothing happened. If you were extremely unlucky, you died from radiation poisoning. And if you were extremely lucky, you got biotic powers.
Kaidan, a biotic caused by the Singapore incident, also mentions that several other such incidents occured over the next few years. While there's never been any proof they weren't genuine industrial accidents, it's very interesting how they never seemed to happen in unpopulated areas...
DC Universe Online has something like this. Lex Luthor comes from the future where he killed the Justice League, only for Brainiac to show up and ruin his party. So he goes back in time to give large numbers of people superpowers to stop his past-self's plans AND Brainiac. The Exobites contain data on all of earths heroes and villains, they are released into the atmosphere infecting random people who can be either good or evil depending on their personality before being infected.
"You there! Have you seen my son go by? He's infected with a terrible virus that will kill one third of the earth's population, making five eights of those remaining lactose intolerant and while granting amazing superpowers to a quarter of the remainder!" ... "Well, come on then, either you've seen him or you haven't." "Wait, no, start over. I was always bad at math."
For those interested, approx. 6.85 billion people in the world (as of July 2010 estimates), that would be roughly 430,265,625 individuals with amazing superpowers or about 1-in-11 people (granted that's after 1-in-3 people have died).
A much smaller-scale version than usual happened in Knowledge Is Power; a Negative Space Wedgie opened up in a cafeteria-type-area on a college campus and granted superpowers to the eight humans currently in it, with the nature of the powers being based on what they were thinking about—their homework.
The Big Bang from Static Shock (and from the original Milestone Comics line that inspired it) would fall under this: the experimental "radioactive tracer gas" that police used during an apocalyptically large gang war left many of those exposed to it with superpowers.
The Nanite Event from Generator Rex. Five years ago, there was an explosion in a research facility, and Nanomachines infected every living thing on Earth. Every so often, the Nanomachines turn something into a mutant, usually mindless and aggressive. And it's not just humans—animals and plants can be mutated, too.