I can't do top 10s for each Doctor, because (for example) I haven't finished all of Classic Who so I probably can't do top 10s for the 1st or 2nd Doctor, but I'll do top 10s for who I can and top 5/etcs for others. Also, stuff is listed in the order it came out, not favorite to least favorite. I will mark my favorite story from each Doctor as I go.
1st Doctor:
An Unearthly Child (1st Episode only)
The Daleks
The Aztecs
The Dalek Invasion of Earth (Favorite 1st Doctor story)
The 10th Planet
2nd Doctor: (for being my 2nd favorite clasic Doctor, I need to watch a lot more of his stuff)
The Power of the Daleks
Tomb of the Cybermen
The abominable Snowmen
The Enemy of the World
The Web of Fear
The Mind Robber (Favorite 2nd Doctor story)
3rd Doctor:
Spearhead from Space (Favorite 3rd Doctor story)
Doctor Who and The Silurians
Inferno
Terror of the Autons
The Mind of Evil
The Daemons
Day of the Daleks
The Sea devils
The Three Doctors
The Time Warrior
4th Doctor:
The Ark in Space
Genesis of the Daleks
Revenge of the Cybermen
Pyramids of mars
The Brain of Morbius
The Face of Evil
The Talons of Weng-chiang (Favorite 4th Doctor story)
Horror of Fang Rock
The Ribos Operation
The Pirate Planet
5th Doctor:
Kinda
Earthshock (Favorite 5th Doctor story)
The Kings Demons
The Five Doctors
Warriors of the Deep
The Caves of Androzani
Time Crash
6th Doctor:
The Twin Dilemma
Attack of the Cybermen (Favorite 6th Doctor story)
Vengeance on Varos
The Mark of the Rani
The Two Doctors
The mysterious Planet
Mindwarp
Terror of the Vervoids
The Ultimate Foe
The End of the Line (This is listed under protest, because I want 10 stories but cannot, in good conscience, put Timelash or Revelation of the Daleks on the list which probably tells you how much I don't like them because I still put Twin Dilemma on the list over another BF story)
7th Doctor:
Delta and the Bannerman (Favorite 7th Doctor story)
Remembrance of the Daleks
The Happiness Patrol
Silver Nemesis
Battlefield
Survival
8th Doctor:
Doctor Who The Movie (Favorite 8th Doctor Episode)
Shada (BBC animation)
Night of the Doctor
War Doctor:
Day of the Doctor
9th Doctor: (two parters are treated like one story for me in the NuWho era)
The End of the World
Dalek (Favorite 9th Doctor Episode)
The Long Game
Father's Day
The Empty Child/The Doctor Dances
Bad Wolf/The Parting of the Ways
10th Doctor:
School Reunion
The Girl in the Fireplace
Gridlock
Voyage of the Damned
The Doctor's Daughter
The Unicorn and the Wasp
Silence in the Library/Forest of the Dead (Favorite 10th Doctor Episode)
The stolen Earth/Journey's End
The Water of Mars
The End of Time
11th Doctor:
The Eleventh Hour
Time of the Angels/Flesh and Stone
Vincent and The Doctor
The Lodger
The Pandorica Opens/The Big Bang
A Christmas Carol (Favorite 11th Doctor Episode)
The Doctor's Wife
A Good Man Goes to War
Let's Kill Hitler
Closing Time
12th Doctor:
Deep Breath
Into The Dalek
Time Heist
The Magician's Apprentice/The Witches Familiar
The Girl Who Died/The Woman Who Lived
Heaven Sent (Favorite 12th Doctor Episode)
The Husbands of River Song
The Pilot
World Enough and Time/The Doctor Falls
Twice Upon a Time