Where there's society, there's a foundation story. And where there's government, there's a holiday to instill patriotism and pride. So here are the ways fiction has commemorated independence from an oppressor, the end of a civil war, or just the day certain documents were signed and the current government came into existence.
First Contact Day, Star Trek
First Contact Day is (will be? Stupid time travel.) April 5th, 2063. On that day, Zefram Cochrane pilots Earth's first warp-capable ship, drawing the attention of a Vulcan ship. Thus, with the words "Live long and prosper" and an extremely awkward handshake, was an alliance begun.
Alternately, you can celebrate it as the day the crew of the USS Enterprise-E traveled back in time, defeated the Borg, and created a remarkably stable time loop to preserve the future as they know it.
Technically, the founding day of the Federation is celebrated on the extremely creatively-named "Federation Day." But First Contact Day is just cooler. Why celebrate the conclusion of what were surely long diplomatic talks when you can commemorate the day a drunk tried to get a trio of Vulcans to dance to "Ooby Dooby"? It would be like the United States throwing over the Fourth of July for Constitution Day.
Colonial Day, Battlestar Galactica
Okay, so this one is a celebration of the conclusion of what were surely long diplomatic talks. Colonial Day marks the date of the official signing of the Articles of Colonization. The Articles of Colonization created a unified government for the 12 colonies, which had each been a sovereign nation before the (first) Cylon War. In response to the Cylon threat, the colonies apparently thought they had a better chance at survival as a unified front. Given the Cylon attack that nearly wiped them out happened 51 years after signing, this may have been a little optimistic. But that doesn't mean the remainder of humanity didn't still celebrate Colonial Day by... electing Gaius Baltar Vice President.
Empire Day and Republic Day, Star Wars
What the galaxy far, far away lacks in creative naming, it makes up for in quantity. If you are Empirically inclined, there's Empire Day. If you're a fan of the Republic, there's Republic Day.
Republic Day is a generic day celebrating the founding of the Old Republic. It falls on the 19th day of the third month, so, for us, March 19th. It is, according to Wookiepedia, "characterized by many fireworks and parades, as well as many stores conducting half-price sales, especially on Coruscant." Woo! The Old Republic was full of partiers.
Granted, Empire Day is more in the vein of "Celebrate — or else." When Emperor Palpatine declared the Republic dead and the Empire alive, he also "mandated that Imperial citizens would celebrate the anniversary of Empire's creation yearly, for the sake of posterity." Some places celebrated for weeks, apparently misunderstanding the word "day." Or not, since the Empire's way of rewarding observance was to promote state pride by giving loyal citizens artwork and food rations. That's right, celebrate hard enough and you might be given food.
And, in a mildly hilarious form of civil disobedience, the Rebel Alliance celebrated "Remembrance Day." How? By celebrating Republic Day on Empire Day.
Unification Day, Firefly
Unification Day marks the day the Alliance defeated the Browncoats in the Unification War. As with a lot of these kinds of holidays, the name is a bit of propaganda by the winners. The fact that years of bloody fighting ended with one side victorious and the other one subject to the winner's control kind of takes the wind out of the idea of "unification." But go with it. Or start a brawl in a bar, like Mal did.
Founder's Day, Eureka
Eureka is a town founded by a group of genius scientists as a "haven for the world's greatest thinkers to live and create." And to celebrate its creation, the town celebrates Founder's Day by putting up exhibits, restoring the cars owned by the founders, drinking Cold War cappuccinos, and engaging in some hardcore historical reenactment, by which we of course mean time travel.
What is it with founding holidays and time travel? Is it because writers can't stand to just talk about the creation of their worlds, they need to have their characters be involved, too? Because the season 4 premiere of Eureka took place on the 60th anniversary of Eureka's founding – Founder's Day – and sent a crop of main characters back in time to the actual founding. To the show's credit, when they returned, they'd affected the past enough to create a new timeline that they then had to live in. Also, they brought one of the founders back with them, played by James Callis, who also played Gaius Baltar. Man, these holidays were good to him, weren't they?
Freedom Day, Futurama
Now, it's never explicitly stated that Freedom Day marks some sort of founding, but it's pretty heavily based on the Fourth of July, is celebrated by/on Earth, and is particularly celebrated in the Earth's capital of Washington D.C. Therefore, you're pretty safe seeing this as a founding holiday.
And why not celebrate by going to the Freedom Day Parade after spending some time naked in the traditional Freedom Tub? And definitely engage in the most important part of Freedom Day: Expressing oneself in any way without consequences. It's like the Fourth of July and The Purge had a baby. However, it is not recommended that you express yourself by eating Earth's flag. It can eventually work itself out, but is probably not worth the hassle in the long run.
Honorable Mentions (days not strictly speaking founding holidays, but close):
• Creator's Day, Discworld
If you participated in the last Ankh-Morpork Revolution (especially if you participated twice, like some people), you are entitled to wear a sprig of lilac on May 25th. The "Glorious Revolution of the Glorious Twenty-Fifth of May" ended the reign of Lord Winder, but also unfortunately brought the reign of Mad Lord Snapcase.
You could also celebrate Patrician's Day on the 6th of Grune.
But the important one is probably April 28th: The Creator's Birthday. Discworld runs on narrative causality: whatever should happen in a good narrative, will. The one in a million shot will never work, so it always does. So of course the day of creation celebrated on Discworld is the day its actual creator, Terry Pratchett, was born.
• Skynet Becomes Self-Aware, Terminator
Not likely to be celebrated by humanity, but a foundational day for society nonetheless: August 29th, 1997, the day Skynet became self-aware.