These are the number of clips from each Doctor. Parentheses are used when it's a clip from that Doctor's episode, but the Doctor's face isn't actually in the clip:

Hartnell - 7
Cushing - 1
Troughton - (1) 8
Pertwee - 8
TBaker - 8
Davison - 8
CBaker - 8
McCoy - 8
McGann - 7
Hurt - 4
Eccleston - 8
Tennant - (3) 9
Smith - (2) 8
Capaldi - (2) 8
Whittaker - (4) 8

Here are the episode references, in order. Parentheses are used when it's a clip from that Doctor's episode, but the Doctor's face isn't actually in the clip:

Capaldi, s09e04 - "Gimme plenty of that guitar"

McCoy, Time and the Rani, P2
CBaker, Attack of the Cybermen, P1
Troughton, Abominable Snowmen, P2
Eccleston, S01e02
Hartnell, Romans, P3 Conspiracy
Smith, s05e13
Tennant, s02e12
Pertwee, Sea Devils, P3 - "Oh, I've been traveling"
TBaker, Shada, P1 - "on a boat"
Davison, Time Flight, P1 - "and a plane"
Pertwee, Daemons, P2 - "in a car"
Smith, s07e06 "on a bike"
(Tennant), Planet of the Dead, 2009 - "with a bus"
(Capaldi), s08e08 - "and a train"
Hartnell, Unearthly Child, P3 Forests of Fear - "Traveling there"
TBaker, Robot, P1 - "Traveling here"
Davison, Snakedance, P1 - "Everywhere"
McGann, Movie, 1996, - "in every gear."
Pertwee, Colony in Space, P4 - "But, oh lord, we pay the price"

(Troughton), Wheel in Space, P5 - "With a spin of the wheel"
McCoy, Silver Nemesis, P2 - "with a roll of the dice"
CBaker, Twin Dilemma, P3 - "Ah, yeah"
(Tennant), Planet of the Dead, 2009 - "you pay your fare"
Troughton, Ice Warriors, P1 - "and if you don't know where you're going"

Capaldi, S09e06 - "any road will take you there"
Whittaker, s11e06
Eccleston, s01e11
McGann, movie, 1996
CBaker, Vengeance on Varos, P1 - "I've been traveling"
Capaldi, S08e02 - "through the dirt and the grime"
Hartnell, Unearthly Child P2, Cave of the Skulls - "From the past"
Whittaker, Thirteenth Doctor Revealed. 2017 - "To the future"
(Tennant/Tardis) s02e13 - "through the space"
TBaker, Ribos Operation, P2 - "and the time"
Tennant, S02e01 - "Traveling deep beneath the waves"
Capaldi, s09e03 - "in watery grottoes"
Pertwee, Planet of the Spider, P5 - "and mountainous caves"
Eccleston, s01e11 - "But oh lord"
TBaker, Androids of Tara, P4 - "We've got to fight"
Smith, End of Time, P2 - "with the thoughts in the head"
Capaldi, s09e06 - "and the dark and the light"
Davison, Castrovalva, P1 - "No use to stop and stare"
Hurt, 50th Anniversary, 2013 - "And if you don't know where you're going, any road will take you there."

CBaker, Terror of the Vervoids, P1
TBaker, Revenge of the Cybermen, P2
Troughton, Krotons, P1
McCoy, Battlefield, P1
McGann, movie, 1996 - "You may not know where you came from"
Cushing, Invasion Earth, 2150
Hurt, Night of the Doctor short, 2013
Tennant, s03e08 - "You may not know who you are"
Eccleston, s01e01
Hartnell, Daleks, P2, The Survivors
Whittaker, Twice Upon a Time, 2017Capaldi, s08e01
Smith, s06e02 - "May not even"

Troughton, Dominators, P3 - "wondered"
McCoy, Battlefield, P1
Davison, Kinda, P1
Hartnell, Daleks, P1 The Dead Planet - "How you got this far"
Whittaker, s11e01
CBaker, Mindwarp, P3
Pertwee, Three Doctors, P1
Troughton, Three Doctors, P1
Tennant, Voyage of the Damned, 2007 - "I've been traveling on a wing and a prayer"
TBaker, Robot, P1 - "By the skin of my teeth"
Smith, Time of the Doctor, 2013 - "By the breadth of a hair"
Eccleston, s01e03 - "Travelng where the four winds blow"
McCoy, Greatest Show in the Galaxy, P1 - "with the sun on my face"
Capaldi, s09e11 - "in the ice"
Troughton, Ice Warriors, P4 - "and the snow"
Davison, Black Orchid, P1 - "But oo-ee, it's a game"
Smith, s05e01 - "Sometimes you're cool"

CBaker, Twin Dilemma, P1 - "Sometimes you're lame"
Hurt, 50th Anniversary, 2013 - "Ah yeah, it's somewhere"
McGann, movie - "And if you don't know where you're going"

Pertwee, Planet of the Spiders, P2 - "Any road will take you there"
TBaker, Leisure Hive, P1
McCoy, Remembrance of the Daleks, P4
Tennant, s02e10
Troughton, Invasion, P3
Whittaker, s11e12
Tennant, Runaway Bride, 2006
Eccleston, s01e02
(Whittaker), s12e01
Capaldi, s10e03
Eccleston, s01e01

Davison, Castrovalva, P2
Hartnell, Unearthly Child P2, Forest of Fear
McCoy, Delta and the Bannermen, P3
McGann, movie
Tennant, s02e12
Pertwee, Time Monster, P3
(Smith), s05e12
(Whittaker), s12e05
(Whittaker), s12e10
Hurt, 50th Anniversary, 2013
(Tennant), s02e12
(Capaldi) s08e09
(Smith) s07e13
Whittaker, s12e01
McGann, movie
CBaker, Mindwarp, P4
(Whittaker), s11e09

Tennant, s04e13
Davison, Arc of Infinity, P3
Whittaker, s11e04
McGann, movie
Hartnell, Reign of Terror, P2, Guests of Madame Guillotine
Smith, s06e04
Tennant, Runaway Bride

Troughton, Invasion, P8
Pertwee, Planet of the Spiders, P2
McCoy, Time and the Rani, P3
Eccleston, s01e01
TBaker, Power of Kroll, P1
CBaker, Mysterious Planet, P1
Davison, Awakening, P1
Smith, Christmas Carol, 2010
Hartnell, War Machine, P3
Whittaker, s11e10