I was discussing with @Tylershads about the Superman reboot, and I wondered how the Justice League was actually formed in the comics. I know that there are several versions of the Justice League. How were the different Justice Leagues formed in each version?

For example, did Superman say "Hey guys, we're all super, so let's team up!"?

The Justice Society

The Justice League of America was patterned after the Justice Society of America, a comic popular in the 1940's with a collection of the greatest heroes of the era getting together against foes no single hero could overcome. The heroes depicted on the cover of All Star Comics #3 include (left to right) the Atom, the Sandman, Spectre, The Flash, Hawkman, Dr. Fate, Green Lantern and the Hourman.

Those heroes were the true inspiration for the Justice League. When asked to revitalize the JSA, the venerable Gardner Fox decided to reinvent the Justice Society with more modern heroes, who were analogs in some cases, of the original heroes. (See Green Lantern - Alan Scott, the Flash - Jay Garrick, the Atom - Al Pratt, and Hawkman - Carter Hall for examples.)

The Justice League

The Justice League - DC Comics greatest and most famous heroes of all time, iconic legends which spawned a generation of four-color comics that transformed the industry since the 1960's. Within months of their arrival, they inspired the Fantastic Four and the Avengers, two of Marvel's most venerable and well-loved superteams.

The original Justice League had their debut in Brave and the Bold #28 (1960) against the non-human, starfish-like alien, Starro the Conquerer. The original lineup was seven characters, Wonder Woman, the Martian Manhunter, Green Lantern, the Flash and Aquaman. While Superman and Batman were requested to join, it would be some time before they would be regulars in the lineup, acting more like honorary members than full-time heroes.

Superman and Batman were downplayed and given less of a billing to allow the other heroes who did not have their own books or were far less popular to shine. The idea of seven major Justice Leaguers would have an affect on lineups of the Justice League for years to come. This debut however is not their origin story. In this story, they act as if they have been working together for some time. Their actual origins would not be revealed until two years had past in Justice League of America #9.

It was revealed the Appellaxians had come to Earth in a ritualistic battle for the fate of their planet. They preferred to have this battle off-world (keeps reconstruction costs down, I guess) and found themselves taking on natural shapes from objects on Earth. In the classic form of the time, the heroes separated to do battle with each individual Appellaxian. When the enemies were defeated they decided to join forces and remain the Justice League of America.

A Glimpse of Things to Come

These two groups would eventually be relegated to entirely different continuities known as Earth-2 for the JSA and Earth-1 for the JLA. The two teams would eventually have an annual meeting across the dimensional boundary started in the famed story: The Flash of Two Worlds. This annual cross-dimensional adventuring would eventually lead to the most famous of the DC Universes reboots ever: The Crisis on Infinite Earths.

And yes, I understand this only covers what would be considered the Silver Age Justice League, pre-satellite, at that. It does not cover:

• 
  Justice League Detroit,


• 
  Justice League International,


• 
  Extreme Justice,


• 
  Justice League of America - Vol 2,


• 
  JLA,


• 
  52, or the


• 
  New 52 Justice League.

I know the previous answer covered the “silver age” team but the question asked for the origins of the multiple incarnations.

Grant Morrison’s Justice League

One popular version was Grant Morrison’s early 2000’s team. It consisted of Superman, Batman, Wonder Woman, Flash (former Teen Titan Wally West), Green Lantern (Kyle Rayner), Aquaman, and Martian Manhunter as the 7 member foundation.

Before the book began, a Justice League like team was in place consisting of Matamorpho and his close allies which did seem to team up with the before mentioned characters often. Everything changed when a group of alien beings called the Hyper Clan arrived on Earth. They claimed to have come out of good intent and even used their powers to turn a section of the Sahara into fertile land, but the other heroes would still view them with suspicion, even immediately assuming they were responsible for the Watchtower being pushed out of orbit.

These suspicions gave fruit when they began to routinely execute superhuman criminals. The seven went to confront them at their arctic stronghold but were immediately subdued, everyone assumed Batman had died in the confrontation. While the rest were in their prison, Batman had taken down one of the Hyper Clan and put a note on his chest (Die Hard style) saying “I know your secret…”, then hidden somewhere in the compound.

The leader of the Hyper Clan shrugs his presence off while Superman states “he is the most dangerous man on Earth.” Batman frees the others and reveals the Hyper Clan is in reality a group of White Martians here to conquer Earth. They use this information—their “Kryptonite” is fire—to defeat them. So a new Justice League is formed!

The New 52

The Justice League forms when Darksied first attacks Earth and Superman, Batman, Wonder Woman, Flash (Barry Allen), Green Lantern (Hal Jordan), Aquaman, and Cyborg, all young new heroes with little experience, gathered to repel his invasion. The Justice League International was formed 5 years after this by the U.N. purely to sway public opinion in favor of big government and consisted of Booster Gold, Green Lantern (Guy Gardener), Ice, Fire, Vixen, Godiva, Rocket Red, August General in Iron, and Batman.

The Justice League of America was created by the U.S. for the excuse that this country needed heroes to serve us the same way soldiers do, but secretly because each member of this team counteracted a Leaguer and the team was put together just in case the original team threatened American interests. The team consisted of Col. Trevor, Martian Manhunter, Green Arrow, Katana, Vibe, Green Lantern (Simon Bazz), Hawkman, Stargirl, Catwoman (unofficial member), and Dr. Light (recruit) and was disbanded after the events of “Forever Evil.”

Well here's the story darksied attacks earth beats up superman wonder women forms the justice league they attack darksied and all lives happily ever after