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

Prince Blueblood thought the Grand Galloping Gala was over. He thought he could just go to sleep and put it behind him. He never expected to be reliving the same disaster of a day, over and over... and over.

TV tropes page here:
http://tvtropes.org/pmwiki/pmwiki.php/FanFic/TheBestNightEver

Thanks to all the people who wrote the page and all the people who gave me a little wakeup call and comment to become aware of that fact! You can't see it, but you guys put a real smile on my face tonight.

Also, recently, extra thanks to RD Dash for giving TBNE a thorough editing. I've updated the fic accordingly (7.11.12)

Twilight isn't having a very good day. An experimental spell blew up in her face, an army of changelings is attacking Canterlot, and she just died. Yet somehow, it looks like it's going to keep going downhill from here.

Given the chance to correct what's gone wrong, Twilight swears she's going to fix all this even if it kills her. Which it will. Frequently.

Cover art by Pixel Prism
Spanish Translation
Series TV Tropes page

Twilight still isn't having a very good day. An army of changelings is attacking Canterlot, and the experimental spell that blew up in her face has stuck her in a time loop until she gets everything perfect and saves Equestria.

She's got a plan. She's also got a problem: Suddenly, she's not the only one whose day is repeating. And when you're caught between unstoppable force and immovable object, life has a tendency to get complicated.

* * *

This story is an authorized alternate-universe re-imagining of Eakin's Hard Reset, in which multiple loopers turn the time shenanigans up to 11. (Knowledge of Hard Reset is not required, but based on reader comments, will help in sorting out the early chapters.)

Cliff's Notes versions: RampantArcana has started a GitHub repository to codify the time-loop rules and the early-story timeline. Hawthornbunny has posted a chapter-by-chapter breakdown of all the loops, including the ones we don't see, with a lot of critical analysis. Those links contain spoilers (of currently posted chapters). If you're confused, either one of those fan projects is a great starting point, and story comments have a lot of insightful discussion as well.

Publication schedule: 2014 kicked my plot, but as of November I'm picking up the writing again and hope to have something by the end of the month.

Cover art by Alexstrazsa.

This story is a sequel to Hard Reset

After the events of Hard Reset Twilight's life and mental well being are slowly returning to normal. Her recovery is cut short, though, when a letter arrives informing her that the time loop spell she cast is causing severe damage to space and time itself. In over her head, Twilight tries to summon anypony who will know how to fix it. The pony she gets is the last one she ever thought she would meet... and nothing like she expected him to be.

Available in Spanish thanks to dgs1993
Series TV Tropes page

This story is a sequel to A Stitch in Time

Having discovered the message left for her by Star Swirl the Bearded in the distant past, Twilight once again finds herself caught up in the middle of a struggle against forces far greater than herself. In order to even stand a chance she'll need to travel further and wider than she ever has, and forge some unlikely alliances with old enemies. All to bring down the powers that have manipulated and shaped her entire life, and retake control of her own future.

The conclusion of the Time Loop Trilogy, which began with Hard Reset
Available in Spanish thanks to dgs1993
Series TV Tropes page

This story is a sequel to You Can Fight Fate

Time loops? The end of existence as we know it? Fate itself conspiring against you? Who has the energy to deal with that kind of thing?

Not Cloud Kicker, that's for sure. She's a mare who knows what she wants out of life. An easy job, a nice house, and an endless supply of potential banging partners. Then one day a simple little flower vendor moves in down the street and everything starts to change.

As a side story to the main Time Loop Trilogy, you can expect massive spoilers in the comments for both the original stories and unwritten chapters of this one.