I haven't read all of these, though I've at least tried to read most of them.  I also don't necessarily recommend all of them either--quite the opposite for a few, in fact--but I've starred the ones that I consider definitely good.

This is the source list for this.

A Simpler Time by DJLowrider

What started as a normal friendly visit ends up taking two ponies on a trip down memory lane that leads them both to realize their friendship began even before Rainbow Dash's first sonic rainboom.

Ah Ain't Got No Ack-cent! by Conner Cogwork

When Rarity is overwhelmed with making designs for an agriculture exhibition, she turns to Applejack for advice. But when she gives Applejack a hair style treatment in return, the apple farmer lets her accent slip from southern drawl to sophisticated Manehattenite. The result? More fancy parties than you can shake a candy apple at!

Anthropology by JasonTheHuman

Humans.

Truth or myth? Ancient lost civilization or just an old pony's tale?

No pony has ever seen one, and most haven't even heard of them. But Lyra knows that these wonderful creatures are more than just old legends, and she's going to find out... and possibly drive her roommate insane in the process.

*Austraeoh by "Imploding Colon"

Rainbow Dash flies east.

*Background Pony by shortskirtsandexplosions

"My name is Lyra Heartstrings, and you will not remember me.  You won't even remember this conversation.  Just like with everypony else I've ever met, everything I do or say will be forgotten.  Every letter I've written will appear blank; every piece of evidence I've left behind will end up missing.  I'm stuck here in Ponyville because of the same curse that has made me so forgettable.  Still, that doesn't stop me from doing the one thing that I love: making music.  If my melodies find their way into your heart, then there is still hope for me.  If I can't prove that I exist, I can at least prove that my love for each and every one of you exists.  Please, listen to my story, my symphony, for it is me."

*Drop of Moonshine by Pen Stroke

After a long day of ruling Equestria, the Royal Sisters need a chance to unwind. Luna's solution is a few glasses of her once famous Moonshine, a drink distilled from moonlight. Celestia has been sober for a thousand years, but the temptation to have "just one" glass proves too great. Yet, when that one glass turns into several, it's Twilight who will have to deal with the princesses when they’re drunk off their flanks.

*Eternal by device heretic

Many years after sending her beloved protege to Ponyville, unease sits heavily on Princess Celestia's heart as her relationship with Twilight Sparkle seems to have cooled despite all they've accomplished together. On the advice of her sister, Celestia sets out to investigate and resolve the lost connection with her most faithful student. What does it mean to be a Faithful Student...or a Princess of the Sun?

***Fallout: Equestria by Kkat

Set in an alternate future, one pony must learn to survive in a blasted, poisoned land... and possibly, with the aid of friends made along the way, bring new light into the darkness of post-apocalyptic Equestria.

Hostile Takeover by Coconutswallow

The Mane-Event, a popular stage show in Manehattan, has acquired a rare creature they intend to use as part of a new act. Their typical animal handlers prove inadequate for the new job so they invite Equestria's best to be the caretaker-- Fluttershy. Moving to a new city requires the inconvenience of finding a new place to stay, however. What fortune that Trixie, one of the primary acts of the Mane-Event, just so happens to have free space at her apartment.

And then the Element of Kindness lived with the Element of Egotism.

It Takes a Village by determamfidd

Spike only wants things to stay the same. Time, however, has other ideas. He's going to need a lot of help... An everypony story.

**It's a Dangerous Business, Going Out Your Door by Jetfire

When an accident leaves Twilight Sparkle seriously ill, Applejack, Rainbow Dash, and Rarity must undertake a perilous journey to find her a cure.  What adventures await them beyond Equestria's borders?

My Little Alicorn by InsertAuthorHere

Luna has had enough of Celestia's games, and has found the perfect means of revenge.  Using a long-forbidden spell, she transforms her sister into little more than a small filly, all so she could pull the greatest prank ever.  Unfortunately, she soon learns that before you fool around with dangerous magic, you really need to read the fine print...

My Little Dashie by ROBCakeran53

When your life is as dull a gray as the world that surrounds you, the mundanities can make it all seem meaningless. Sometimes all we need is a little color -- or six -- to reintroduce us to what truly makes life worth living.

*Naked Singularity by Cold in Gardez

Twilight Sparkle is a gifted student and scholar. When she attempts to harness her creative side by writing a science-themed sensual romance novel, however, things rapidly get out of hoof. Can her friends stage an intervention before she humiliates herself (and them) at a prestigious literature recital?

No. No, they cannot.

On a Cross and Arrow by Conner Cogwork

Twilight and her five friends are transported during a botched spell, across dimensions to... Ponyville, Equestria? But not the same one that they knew. Sitting on a bench is Harpsy and Babar. The Doctoress avoids apples from an aspiring Applebuck. And in a library across town, six stallions join their forces as they try to decipher the appearance of filly look-alikes of themselves around Ponyville!

Past Sins by Pen Stroke

On a dark night filled with even darker magics, an insane cult attempts to give Nightmare Moon a body and life of her own, utterly separate from Princess Luna. But, when the spell is interrupted by Celestia, something unexpected is created.

Now, a little black alicorn filly named Nyx finds herself living under the care of Twilight Sparkle, only to be haunted by memories and emotions from her past. Is she Nightmare Moon reborn or is she simply a doppelganger with a soul and mind of her own? Can Twilight Sparkle protect Nyx from those who refuse to see past her dragon eyes and black coat?

Or, will Nyx be forced to inherit the sins that may not even be hers and become the greatest evil Equestria has ever known?

Pinkie Watches Paint Dry by AbsoluteAnonymous

Pinkie Pie has an existential crisis while painting her room.

Rainbow Factory by AuroraDawn (or the much more lighthearted Rainbow Dash Presents version, Captain Hook the Biker Gorilla by FiMFlamFilosophy)

Nopony truly knows how Rainbows are made in Equestria. But when Scootaloo and her friends fail their flight tests, they'll find out the truth to how the glorious Cloudsdale produces it's signature export... and at what horrifying cost.

Story of the Blanks by Aoshi Stark, based on the original game by Donitz

While on her way home from a day with her friends, Apple Bloom runs into Twilight on a trip to Zecora's hut. After insisting to join her, little Apple Bloom gets lost in the woods after chasing a mysterious mare hiding amongst the poison joak. She stumbles upon a town completely isolated within the Ever Free Forest, but something about this town just doesn't feel right...

*Sunny Skies All Day Long by PhantomFox

Princess Celestia tires of constantly being surrounded by decorum, deference, and formality, and decides to take a day off from being Princess.  But visiting Ponyville incognito is harder than she expects.  Will she be able to fit in and make friends without blowing her cover?

The Best Night Ever by Capn_Chryssalid

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.

**The End of Ponies by shortskirtsandexplosions

A lone pony of a Wasteland future Equestria finds a way to visit her dead friends in the past.

The Star in Yellow by Blueshift

Deep in the Royal Library is a book. A terrible book that is said to send whoever reads it mad. A book so dangerous that it has to be hidden away and secured with chains to prevent it from ever being opened.

A book which has just been accidently checked out by Spike on behalf of Twilight Sparkle.

The Star In Yellow is rising once more, and only Rainbow Dash and Spike can save Twilight before it's too late. Ideas live forever. Ponies do not.

*The Sweetie Chronicles: Fragments by Wanderer D

Be Awed and Amazed by the tale of Sweetie Belle as she traverses the multiverse in search of her lost mentor and friend, Twilight Sparkle! Will she find her in post-apocalyptic Equestria? Or maybe in a strange world where everypony is the wrong gender? Or even where a Pony claims to be a human? Read as she journeys through very familiar worlds you might have read about... if you dare!

Upheaval: Breaking Point by Visiden Visidane

Equestria is a land of magic and harmony, a peaceful realm ruled by immortal,benevolent monarchs. But at what cost is this possible? A fateful encounter leads Twilight Sparkle to find out exactly how.

Fake answers:

Allegrezza by CoffeeGrunt

Octavia is a high-class pony. Fine alcohol is her wont, and uncouthness her intense chagrin. Such is her surprise to find herself lumbered with an insufferable oaf of a DJ pony. However, sometimes these situations work themselves into a satisfactory ultimatum all the same.

Antipodes by PK

Set in the far future after Celestia and Luna mysteriously vanished and the sun and moon froze in the sky, Antipodes the the story of two ponies thrust out into the harsh new world on an adventure to uncover what happened to the world so long ago.

Keeping Your Hooves on the Ground by InsertAuthorHere

The Cutie Mark Crusaders ask Rainbow Dash and Fluttershy about what happened just after the events of the Cutie Mark Chronicles; specifically, what happened to Fluttershy and Rainbow Dash immediately after the race.  Reluctantly, Dash and Fluttershy delve into a tale.  A tale of a young Fluttershy's amazement at the world she had landed upon, and a filly Dash's desperate quest to save her from that most evil of places: THE GROUND.

*Martial Bliss by Skywriter

Shining Armor learns the most important tactical lesson of his life.

*Night Guards by Raugos

At first glance, Princess Luna's charioteers might appear to be little more than Royal Guards dressed in festive apparel for Nightmare Night. However, there is far more to the story than that - the Night Guards once played a pivotal role in the history of Equestria, and have sacrificed more for their beloved princess than most ponies are even aware of.

Petriculture by Kwakerjak

In an effort to keep her mind occupied, Twilight Sparkle decides to delve once again into the grand mysteries of Pinkie Pie. This time, Twilight's focus is on her claims of growing up on a rock farm: like so many things related to Pinkie Pie, the idea that somepony could grow rocks as an agricultural product makes absolutely no sense. However, the investigation eventually leads Twilight to a rather... surprising discovery.

Progress by Andrew Joshua Talon

A thousand years is quite the generation gap, so Princess Luna decides she has to get with the times. However, this isn't quite as easy as she thinks it will be...

Rest Stop by JohnPerry

At a rest stop on her way to Appleloosa, Twilight Sparkle has a rare moment to reflect...

Shipping and Handling by Pegasus Rescue Brigade

When Ditzy Doo loses her job at Cloudsdale Mail and Freight, she gets a job at another shipping company... only to find out their definition of shipping has nothing to do with delivering packages! Desperate for income to support herself and Dinky, will Ditzy be able to make it as a pony matchmaker?

Simply Rarity by Somber

An argument between her friends has brought to question Rarity's generosity. Can a unicorn who's had everything and nothing truly be generous?

Somewhere Only We Know by PatchworkPoltergeist

Every night, in a little stable just outside of town, an old mare lays down to sleep. And every night she has the same dream of rainbows and open sky...

The Battle of Fort Book by PinkamenaPiePrincess

Twilight Sparkle's imagination as a child was unbelievable, probably due to all those books. Which also make up the amazing Fort Book, Twilightopia's first stronghold against the country of Armor! With the help of Captain Smartypants and Private Cadence, General Twilight defends her fort against her brother's advancing army of one!

*The Conquering of Love by Littlecolt

Twilight Sparkle finds herself inside a cocoon in the throne room of Canterlot Palace along with her friends and many other ponies. She is thrust into a dream world by Chrysalis who is feeding on the feelings of love and friendship she and the others will experience in their alternate realities. In her dream, she finds Princess Celestia, who has been able to cross between dream worlds. Twilight and Celestia must now travel between dreams in order to awaken their friends and stop Chrysalis. However, some dreams are not as happy as they expected, and some secrets held in the subconscious may be better left unawoken.

The Moonstone Cup by Cyanide

Twilight is invited to Canterlot to compete with some of the greatest magicians in the world for the Moonstone Cup, a prestigious award for the most powerful and skillful magicians, unicorn and otherwise. Can she win? What sort of competition will she face?