This is a fic based on the Time Loop Files, the format of which was first codified by Innortal on fanfiction.net.
Here's a brief guide.
The basic idea is, one character (the Anchor, usually the main character of a fictional setting) is looping back to the very first moments of their parent series every time either they die or some kind of time limit expires. They of course end up monumentally stir crazy given enough time.
Eventually others start to loop as well.
The reset is not always perfect. Sometimes a loop's history will be different to the "prime" loop, or canonical plot.
"Crossover" or "Fusion" loops also occur, randomly. These can involve the home loopers having a guest, or the anchor for one universe spending time in another, or replacements of one character by another.
Vacation Loops are where the Anchor (or others) decide/s "buck it" and lets off steam by doing whatever comes to mind. There's little or no attempt to maintain the original timeline.

In addition, and particularly more recently, it should be known that this story has a collaborative element to it - people may submit loop ideas or loops, ideally at the Spacebattles thread (a link to the current version of which is on the Trope page), and they may become included.

There's two page image options, thanks to Filraen - the current page image has been edited by the original creator from this work of theirs.. The other one is here:
http://hourglass-vectors.deviantart.com/art/MLP-Loops-466030169

The story is generally the same. A group of ponies go on a quest to stop an insane alicorn who had escaped banishment, learning about friendship along the way and mastering the Elements of Harmony. But the details...

It can be Trixie Lulamoon leading the Elements of Harmony against Corona.
Rainbow Dash could be Celestia's student and go to Ponyville.
Equestria could have a deep connection to three young people in its distant past.
The Elements of Harmony could have been moved to Manehattan for the ponies to quest for.
Princess Cadance might rule over an Equestria of music, with Octavia as her prized protege.
Or Spike and Twilight might have their roles reversed, the former a stallion and the Element of Magic.

And each one has been chosen by Discord, an Element removed to a seventh Equestria for purposes as yet unknown. Can they survive? Can they get home? Read and find out!

The Lunaverse was created by RainbowDoubleDash and is used with permission. Opening segment was written by Talon and Thorn.
The Hasbroverse was created by RK_Striker_JK_5 and is used with permission.
The Manehattanverse was created by Little Jackie Papercut and used with permission.
The Cadanceverse was created by GrassAndClouds2 and used with permission.
The Flipverse was created by Bed Head and used with permission.
The Dashverse was created by Trinary and used with permission.

And special thanks to dramatic_spoon for getting this all together.

Twilight wakes in the middle of the night, haunted by a terrifying dream—one that's not so hard to see coming true. One that whispers of a grand destiny awaiting her as a reward for all her hard work, discipline, and noble sacrifice.

But what if she doesn't want a grand destiny?

Snails has a problem - he's been getting headaches, a lot of them, that keep him from sleeping. Trixie is quickly able to identify the problem: He isn't using enough magic, and it's building up. All Snails has to do is use more magic, and the headaches will go away. Of course, the Great and Powerful Trixie is more than willing to train a foal in the use of magic - after all, she's already training Dinky. What's one more?

...wait, why are there seven foals? Help!

A Lunaverse story.

Waking up in an alternate universe in which you are a supervillain can be hard.

Finding out your friends are rebels trying to kill or overthrow you isn't very easy to deal with either.

But trying to solve the situation? That's a real horn cracker.

On one of her regular hunts for gemstones, Rarity discovers a treasure trove beyond her wildest dreams... and the lavender-scaled dragon who collected it. Despite a rocky first meeting, Rarity and Greenfire soon find themselves drawn to each other more and more. But the question remains: How did a young dragon end up in the Everfree Forest all alone?

An alternate universe story that puts our favorite purple dragon and his beloved fashionista into a slightly different situation. Art used with permission from the wonderful ArtisteFish!

Now with a TV Tropes page! Thanks go out to Poptard and whoever else might feel like editing it.

Fan Works
Climbing the Cliff by Pia-chan (from chapter 5)
Such a Pleasant Chat by Fukaï
Some Form of Tea by Pia-chan (from chapter 4)
Promo Animation by CMagic (mild chapter 6 spoilers)

Mayor Mare, newly-minted Mayor of Ponyville, has big dreams and big plans for her hometown. Now all she needs to do is to navigate the entrenched interests, bureaucratic resistance and political pitfalls that stand in her way. And to top things off, on her first day the Mayor finds out that Princess Celestia is sending her prize student over...

Overarching Themes:
Season 1: Land Reform
Season 2: Democracy
Season 3: Reconciliation

A series of stories, corresponding with every MLP episode (if all goes well), from the view of the bureaucrats at Town Hall. Will try and stay true to canon. (EDIT: With 2 semi-exceptions: 1) Cheerilee is Mayor Mare's daughter, and 2) Princess Celestia is much more uptight when negotiating with officials.)

Inspiration from daily life, the UK series 'Yes, Prime Minister', and to the 'Letters from a Disgruntled Friendship Student' fanfic series by milesprower06.