First, I should note that I’m less familiar with the Eleventh Doctor than I am with the Ninth and Tenth Doctor, so this list is probably not comprehensive. I’m spending some time rewatching series 5-7, and I bet this list will change at the end of that. Second, it seems that my choices are very different from other people’s choices, as I had a hard time finding videos of the scenes I like. Ah well.
“The Eleventh Hour” – The Doctor vs. the Atraxi: In the modern series, each new Doctor’s introductory episode does a great job of establishing the character of the Doctor, and this one is no exception. From this scene, we see exactly who the Doctor is: his bombastic nature, his courage, and his disdain for his enemies, and he completes his costume.
“The Big Bang” – Timey-wimey: What I mean here is how the Doctor escapes from the Pandorica, saves Amy, and then saves the universe through the creative use of time travel. The “scene” is something like twenty minutes long, so it’s probably a good thing I didn’t find a video for it. When you first watch this episode, this sequence of events (actually, it’s more like a big ball of events) breaks your brain, but when you think about it, it all works out and it’s brilliant.
“A Christmas Carol” – The Doctor goes back to young Kazran: This episode was fantastic, and there are tons of scenes that I’m sure others would point to as better, but my favorite is when the Doctor gets old Kazran Sardick to start watching the movie, then walks out of the room and appears in the window in the movie. It’s another scene that highlights the non-linear nature of the Doctor’s thinking.
“The Doctor’s Wife” – The Doctor realizes who Idris is: I prefer this scene to any of the other emotional Doctor/Idris scenes. The Doctor is still figuring out how to relate to Idris, and Idris is still figuring out how to be a living creature. Gorgeous.
“The Almost People” – The Ganger Doctor appears: I love it when the current Doctor’s actor is given the opportunity to do their own interpretation of previous Doctors. It doesn’t happen often – the Fifth Doctor just after regeneration comes to mind – but it’s always cool when it happens.
“Nightmare in Silver” – The Doctor vs. the Cybercontroller: I couldn’t find a good video for this, so I had to take what I got. Mr. Smith’s performance as the two very different characters is just amazing.
“The Night of the Doctor”: Ok, I’m sorry, this isn’t the Eleventh Doctor, but this minisode was published during his tenure, so I counted it. This minisode is fantastic. It answers so many questions about how the Doctor got involved in the Time War, and in only a few minutes, establishes for a whole generation of viewers the personality of the Eighth Doctor. It also gives the Eighth Doctor a beautiful end (sacrificing himself, yet again, for the greater good) and fills in the lacking regeneration.
“The Day of the Doctor” – Firing the Moment: While there are plenty of other scenes in this episode that I love, this is the absolute best. After the centuries of self-recrimination of their actions in the Time War and denying the existence of the War Doctor, and then after meeting him again, the Tenth and Eleventh Doctors return to the Time War and support him. They have realized that he made the hardest decision in the universe, and, by joining him at the Moment, show him that they no longer deny him, that they believe in him and are willing to make that decision again, right alongside him.