There are many episodes that’s brought a tear or two while watching, I say “are” because re-watching the episode gives the same response. The biggest was probably Vincent and the Doctor, a very emotional episode with The Doctor and Amy dealing with Vincent Van Gogh and some of his issues and fears. Just thinking about it gives me chills… Spoilers follow!
The scene is at the end, with The Doctor is talking to a Museum curator with Vincent listening in:
The Doctor: I just wondered, between you and me, in 100 words where do you think Van Gogh rates in the history of art?
Dr Black (museum guy): Well… big question, but to me, van Gogh is the finest painter of them all; certainly the most popular great painter of all time: The most beloved; his command of colour; the most magnificent. He transformed the pain of his tormented life into ecstatic beauty. Pain is easy to portray, but to use your passion and pain to portray the ecstasy and joy and magnificence of our world… no one had ever done it before. Perhaps no one ever will again. To my mind that strange wild man who roamed the fields of Provence was not only the world’s greatest artist, but also one of the greatest men who ever lived.
- Turn Left – A few different parts, this is my favorite episode.
- A Good Man Goes to War – When River Song makes the big reveal to Amy and Rory (every time, and I think I’ve watched this one 17 times now).
- Doomsday – When Rose and The Doctor get separated forever.
- Silence in the Library / Forest of the Dead – Not the first few times I watched it, but now that things from the future (River’s past) have been revealed it has a lot more significance.
- The End of Time – David Tennant’s last episode, lots of goodbyes at the end.
But none of those (except the VIncent episode) can really be watched unless you’re a fan already. I’m sure there are more, but these are some of the episodes that I’ve watched a lot, so I’ll limit it to this list.
This is from the 10 day Doctor Who Challenge, which I can’t reference because I have no idea where I found it. I’ve found other 10 day DW and 30 Days, but while similar questions are there, none are identical.