Fleeing from the Time Lords the Doctor accidentally damages the barrier between his own universe and that of Equestria an event that may lead to disaster for both universe. Now each of his incarnations must visit Equestria to repair the damage.

Each chapter will involve a different incarnation of the Doctor and may be posted out of order.
As the normal category/character rules don't work with an anthology, I'm going to list any extra ones for each chapter below.

Part of RainbowDoubleDash's Lunaverse, my entry for the April Crossover writing contest.

Chapter 1 - The Grandfather
The first incarnation of the Doctor and his granddaughter Susan arrive on Equestria and meet Cheerilee and a group of foals on a trip to Whitetail woods. However, can the escape from the monster lurking there?
Categories - No extra
Characters - The Doctor, Susan, Cheerilee, Snails, Scootaloo, Dinky

Chapter 2 - The Cosmic Hobo
The second Doctor and Jamie find themselves helping to defend an arctic research station from an attack from strange ghostly shapes and Ice ponies.
Categories - No extra
Characters - The Doctor, Jamie, Shining Armour

Chapter 3 - The Gentleman
The third Doctor and Jo arrive at Canterlot in the winter and meet the stage magician Quartermoon the Magnificent and his granddaughter Trixie. There appears to have been a rash of mysterious deaths among the magic profession, with Quartermoon be next?
Categories - No extra
Characters - The Doctor, Jo Grant, Trixie, Quartermoon

Chapter 4 - The Bohemian
The fourth Doctor and Leela become part of the Ponyville weather team and take part in a Pegasus game called Sky Tag along side Raindrops and Dash. But another team are playing for keeps and figures from both Raindrops and Dash's past are taking part as well. Can our hero's win out?
Categories - Comedy, Slice of Life
Characters - The Doctor, Leela, K-9, Raindrops, Rainbow Dash, Hoops, Score, Dumb Bell

Chapter 5 - The Good Sport
The fifth Doctor along with Tegan and Nyssa arrive at Canterlot in time for the final of the first annual servants hoofball league. With the shard as the prize the Doctor is forced to enter but other groups as well as the opposing team are working against him.
Categories - Slice of Life
Characters - The Doctor, Tegan, Nyssa, Night Vision, Pinkie Pie, Blue Blood, Luna, Octavia, Paperweight.

Chapter 6 - The Multi-coloured Man
The sixth incarnation of the Doctor and his companion Evelyn interrupt a dinner party at Fluttershy's resulting in her fleeing into the Everfree Forest. Can Carrot Top and the time travellers find her before something terrible happens?
Categories - Comedy
Characters - The Doctor, Evelyn, Carrot Top, Rarity, Fluttershy, Angel.

Chapter 7 - The Chess Master
Twilight Sparkle thinking the Doctor is a threat to Equestria is traveling through time to stop him at every turn resulting in a much darker future. Can The Doctor and Ditzy Doo stop her and prevent disaster?
Categories - Sad
Characters - The Doctor, Ace, Ditzy Doo, Twilight Sparkle.

Chapter 8 - The Bon Vivant
The eighth Doctor and Izzy have little trouble finding the shard and decide the spend the day wandering Ponyville. But has something followed them from their universe and what sweet creature is waiting to be born beneath Bon Bon's store?
Categories - Dark
Characters - The Doctor, Izzy, Lyra, Bon Bon.

Chapter 8.5 - The Soldier
The time war comes to Equestria.
Categories - Dark, Gore, Sad, Tragedy.
Characters - The Doctor, Trixie, Pokey Pierce, Luna, Shining Armour.

Chapter 9 - The Survivor
Fresh from the Time War the new Doctor is a broken man looking for a reason to carry on after the horrors he witnessed and caused. He finds Equestria in the wake of a Discordian led uprising. Will a meeting with Princess Celestia strengthen him or destroy him totally?
Categories - Dark, Tragedy.
Characters - The Doctor, Celestia, Luna.

Chapter 10 - The Darkness Within
The Tenth Doctor and Martha help a member of the Night Guard prevent an assassination attempt on Princess Luna but is the fate of their ally pre-ordained?
Categories - Sad
Characters - The Doctor, Martha, Luna, Nocturne

Chapter 11 - The Eternal Child
The Eleventh Doctor has settled down in Ponyville for some time to carry out some experiments but when part of his equipment gets away from him it sets in motion a chain of events which results in Greengrass becoming the ruler of Equestria. Can he and Pokey work together to put things back the way they should be?
Categories - No extra
Characters - The Doctor, Pokey, Greengrass, Notary

This story can be read in various orders, the above is in the order that it occurs to the Doctor but not the order it was written or the order events occur on Equestria.

I set myself the goal of never writing two adjacent doctors after each other, which meant that some idea's weren't written until long after they were thought up, particularly the 4th Doctor story was one of the first conceived but one of the last written. The order the story was written in was: -

1st Doctor
6th Doctor
3rd Doctor
8th Doctor
5th Doctor
10th Doctor
2nd Doctor
7th Doctor
4th Doctor
11th Doctor
8.5th Doctor

The order of events on Equestria is a bit more complicated due to time travel. The 7th Doctor story happens at the same time as many of the other chapters as well as other times: -

7th Doctor - c. 20000 BFC (Before the fall of Corona)
9th Doctor - 120 BFC
3rd Doctor - 990 AFC (After the fall of Corona)
2nd Doctor - 995 AFC
1st Doctor - 1000 AFC (Spring)
6th Doctor - 1000 AFC (Spring)
4th Doctor - 1000 AFC (Summer)
8.5th Doctor - 1000 AFC (Summer) (Alternative Universe)
7th Doctor - 1000 AFC (Summer) (Alternative Universe)
8th Doctor - 1000 AFC (Summer)
11th Doctor - 1000 AFC (Summer)
5th Doctor - 3 CR (Celestia's return)
7th Doctor - 18 CR