Here is a list of favorite scenes from the Tenth Doctor, who, I should note, is the Doctor I know the best, so the list is longer than you might expect. This list is in broadcast order, not in any ranking order.
“The Christmas Invasion” – The Doctor appears: From “Did you miss me?” to “No second chances. I’m that sort of a man,” the Doctor keeps up what amounts to a twenty minute monologue which demonstrates to us exactly who he is.
“School Reunion” – Sarah Jane meets the Doctor: Just beating out John Smith’s stunned babbling when seeing Sarah Jane for the first time in hundreds of years, this scene has Sarah Jane confronting the man who ran out on her thirty years before. Ms. Sladen switches beautifully between surprise, hope, love, and anger, all in the course of a short couple of minutes.
“The Girl in the Fireplace” – The Doctor is stranded: This is one of the episodes in which my favorite scene is probably very unexpected. The Doctor looks up at the stars, realizing that he’s now living with the humans just like they do, and may never return to the TARDIS and the rest of the universe again. He starts to think about what that really means, and how he’s going to survive. I couldn’t find a video that showed just this one scene.
“The Age of Steel” – Mickey triumphant: Once the Doctor regenerated into his tenth form, he started to respect Mickey more, though he still always put him down. At the end of this episode, the Doctor instructs Mickey clandestinely on how to shut down the Cybermen, relying on his computer skills. Mickey succeeds and then rescues them all from the exploding factory. Mickey finally comes into his own right here.
“42” – The Doctor in the stasis chamber: Fighting back against his possession by the sentient star, the Doctor instructs Martha to put him in the stasis chamber. He cries out, “I’m scared! I’m so scared!” and it’s not because he’s afraid of dying, but because he knows that if he loses the battle, he’s going to kill everyone on board. The Doctor showing fear is chilling, and the reason for it is still so the Doctor.
“The Family of Blood” – The Doctor returns to Nurse Redfern: For all of the wonderful scenes in this, my favorite episode, the final scene with Nurse Redfern is still the best. After we’ve watched an hour and a half of Mr. Tennant as John Smith, the human teacher living his life and falling in love, now he’s back to playing the Doctor, and the contrast between them is startling. Even though he’s no different than the Doctor in any other episode, he feels alien here, and perhaps for the first time we truly realize that he doesn’t think and feel like humans do. He invites Nurse Redfern to travel with him, in an attempt to give her hope and love, but only succeeds in being cruel, because as the Doctor, he can’t truly understand her. (The video link only shows half of the scene. The other half can be found by the same poster, under “scene 16.”)
“The Last of the Time Lords” – The death of the Master: I really don’t have much to say about this one. It makes me cry every time.
“Time Crash” – The whole thing: I’m just going to call this one long scene and say that everything about it is wonderful: the writing, the acting, the humor, the interactions between the two Doctors, the tribute to the Fifth Doctor. If I could call it an episode, it’d be at the top of my favorite episode list.
“The Fires of Pompeii” – “Donna, human, no!”: From the Time Lord and the audience perspective (because we know how the laws of time work), Donna may be wrong, but this scene establishes the lengths she’s willing to go through when she thinks she’s right. She’s willing to stand up to the Doctor and fight, without whining or complaining, and without backing down.
“The Poison Sky” – Luke saves the Doctor: Two things about this scene. First, Luke, the completely unlikable genius, redeems himself, without fanfare or heaps of schmaltz. Second, when the Doctor returns from the Sontaran ship, Martha hugs him and Donna punches him. They are completely in-character, and it’s little things like this that make this show so good.
“Journey’s End” – Genesis of the Meta-Crisis Tenth Doctor: Not the actual birth of the MCTD, but the interaction between him and Donna. Mr. Tennant and Ms. Tate work together so well, and to top that off, Mr. Tennant plays the Tenth Doctor with Donna’s mannerisms. Excellent performances from both of them. Sadly, I couldn’t find a video for this.
“The Next Doctor” – Jackson Lake’s story: Jackson Lake’s story is so beautiful, and David Morrissey’s performance in this scene is heartrending.
The End of Time – Four knocks: For all that I love the end of The End of Time, from the moment Gallifrey appears to the Doctor’s regeneration, the best scene from it is when Wilf knocks and the Doctor realizes that he hasn’t escaped his fate. For once, the Doctor voices the thoughts he normally keeps inside: that he doesn’t want to die, he wants to keep fighting, that he wonders what makes someone else’s life more valuable than his own, and, finally, that he’s lived too long. Then, like the Doctor always does, he sacrifices himself for someone else. I couldn’t find this video either.