Beware, there may be spoilers if you haven't watched certain series.
Middle EarthThis is where it all starts. We all know that after the events of The Lord of the Rings the Elves, Gandalf, Frodo, and Bilbo left. Other races were forgotten. The Men became a mighty race again and eventually become the modern society we know now.
Battlestar GalacticaThe Cylons have said it plenty, "All this has happened before, and all of it will happen again." Earth is wasted by the Cylons.
This is where it gets tricky and starts to split into different series. There are 3 portions to this universe.
Battlestar Galactica/CapricaThe Earth (also known as Kobol) was destroyed by the Cylon and Humans escaped to space, developing the 12 Colonies of Kobol.
CapricaThe 12 Colonies of Kobol have established themselves on different planets. Graystone, repeating history, begins to develop Cylons again.
Battlestar GalacticaThe Cylon wars happen, they go their separate ways, the Cylons attack, the Colonies are destroyed, and the remaining humans escape. They eventually make a deal the with Cylons, settle on a new Earth, and start the cycle over.
FireflyThere's a 13th Tribe that's said to have separated from the rest of the Tribes on Kobol and settled on Earth. Well, honestly no one knows what actually happened to them. Except, they just ended up in another part of the universe and developed into the Alliance of the Firefly Verse. (Granted, the origin story of the show is that the population of earth became to great so humans migrated into space, but government lies and they really don't know at this point what happened to Earth That Was.)
SerenityAfter the events of Serenity it's been revealed that the Alliance is evil and a new government must be formed.
Star WarsThe government always ends up evil, right? Basically the Alliance ended up becoming the Galactic Empire and now we've got the Rebel Alliance (the version of Browncoats) fighting them. General Star Wars storyline happenings, the end of this portion of the universe.
The City of EmberHumans knew something was about to happen to the Earth. They prepared and created great colonies underground where the send people to survive the coming tragedy. They eventually emerge from Ember, not really knowing what happened to the Earth, and they begin to setup shop again.
The Hunger GamesOnce the people of Ember (and obviously there had to be other underground colonies, plus the people who survived on the surface) begin to repopulate the earth a government must be set up. We get Panem, the Capitol, and the 13 Districts (note the reocurrance of 13). The whole Hunger Games trilogy happens, the Capitol is overthrown and a new, happier, government emerges.
Star TrekAfter Zefram Cochrane makes first contact with the Vulcans (who have obviously been hiding out from the Galactic Empire and the Alliance because those folks are all uncivilized nut jobs). The Federation is eventually formed.
My husband postulated the possibility that The Matrix could also exist within the same world. I've theorized that perhaps a Cylon escaped into one of the underground colonies and created the Matrix. However, this would mean that for some reason they never managed to emerge from their colony. It's plausible.
Here's a timeline to show how this is all happening at relatively the same time: