There aren't many options for where these scenes could have been taken from, so it's fairly easy to narrow down. In order of the images in the question:
It's a lousy picture, but the line clearly identifies the first picture as the Seventh Doctor, from "Remembrance of the Daleks". The line is one of my personal favourites from the whole show (the bit in The Magician's Apprentice is bolded):
Davros: The Daleks shall become Lords of Time! We shall become all...
Doctor [cutting him off] ...Powerful. Crush the lesser races. Conquer the galaxy. Unimaginable power. Unlimited rice pudding, et cetera, et cetera.
Doctor Who Season 25 Episode 1: "Remembrance of the Daleks"
Next is clearly the Tenth Doctor, and "The Stolen Earth":
Davros: I have my children, Doctor. What do you have, now?
Doctor: After all this time, everything we saw, everything we lost, I have only one thing to say to you. Bye!
Doctor Who Series 4 Episode 12: "The Stolen Earth"
The atrocious hair identifies the Sixth Doctor, and "Revelation of the Daleks":
Davros: I never waste a valuable commodity. The humanoid form makes an excellent concentrated protein. This part of the galaxy is developing quickly. Famine was one of its major problems.
Doctor: You've turned them into food?
Davros: A scheme that has earned me great acclaim.
Doctor: But did you bother to tell anyone they might be eating their own relatives?
Davros: Certainly not. That would have created what I believe is termed "consumer resistance."
Doctor Who Season 22 Episode 6: "Revelation of the Daleks"
Finally, and most prominently, the Fourth Doctor and the classic "Genesis of the Daleks":
Doctor: Just touch these two strands together and the Daleks are finished. Have I that right?
Sarah: To destroy the Daleks? You can't doubt it.
Doctor: Well, I do. You see, some things could be better with the Daleks. Many future worlds will become allies just because of their fear of the Daleks.
Sarah: But it isn't like that.
Doctor: But the final responsibility is mine, and mine alone. Listen, if someone who knew the future pointed out a child to you and told you that that child would grow up totally evil, to be a ruthless dictator who would destroy millions of lives, could you then kill that child?
Doctor Who Season 12 Episode 4: "Genesis of the Daleks"
There's one more soundclip that plays, although the Doctor in question doesn't get a moment on screen (or, if he does, it's only a momentary flash). The line itself is a little garbled, since it plays more-or-less concurrently with another Fourth Doctor line from "Genesis of the Daleks", but careful watching (and some help from Chrissie's Transcripts Site) reveals that it's the Fifth Doctor and "Resurrection of the Daleks":
Doctor: Until I walked through that door, I foolishly hoped you'd changed enough for me not to have to do this.
Davros: Stien, kill him!
Doctor: I'm not here as your prisoner, Davros, but your executioner.
Doctor Who Season 21 Episode 4: "Resurrection of the Daleks"