The Tag of "The Wedding of Sarah Jane Smith", one of the last filmed appearances of David Tennant as The Doctor:
The Doctor: Don't forget me, Sarah Jane.
Sarah Jane Smith: No one's ever going to forget you.
The look on Sarah Jane's face as Peter renounces his agreement with The Trickster is both this and a Tear Jerker.
Seeing the Brigadier in "Enemy of the Bane" after so many years. The looks on Nicholas Courtney and Lis Sladen's faces must be seen to be believed. Sladen and Courtney had seen each other somewhat regularly at conventions, but it's entirely possible that the last time we saw Sarah Jane and the Brigadier onscreen together was the last time Sarah Jane and the Brigadier saw each other. Moves into heartbreaking Tear Jerker territory, though, after 2011... and yet how fitting that it's these two who were reunited so shortly before we lost them both for good...
The Brigadier: (reverently) Sarah Jane Smith.
Sarah Jane: (warmly) Hello, Sir Alistair.
Any time Luke and Sarah Jane are reunited. Hell, just the entirety of Luke and Sarah Jane's relationship, period.
The Nightmare Man, where Sarah Jane asks K-9 (her only companion until Luke and the other entered her life) to look after Luke while he's at school.
Mr. Smith admiting that he's going to miss K-9.
The moment in Death of the Doctor when you can almost see Russell T Davies think "to hell with it" as he dives into the Continuity Porn:
Sarah Jane Smith: There’s a woman called Tegan in Australia, fighting for Aboriginal rights. There’s Ben and Polly, in India, running an orphanage there. There was Harry... oh, I loved Harry. He was a doctor, he did such good work with vaccines. He saved thousands of lives. There was a Dorothy something. She runs that company, A Charitable Earth. She’s raised billions. And this couple in Cambridge. Both professors. Ian and Barbara Chesterton. Rumour has it, they’ve never aged. Not since the sixties. I wonder... echoes of the Doctor, all over the world. With friends like us, he’s never going to die, is he?
Similarly, Eleven's speech to Jo earlier in the episode.
Jo: So you've been watching me? All this time?
Eleventh Doctor: No. Because you're right - I don't look back, I can't. But the last time I was dying, I looked back on all of you. Every single one. And I was so proud.
What makes it more heartwarming, is that Jo was somewhat in doubt about him being the Doctor, and that speech confirmed he was indeed her Doctor
After spending the most of the first part thinking the Doctor is dead, the reunion between the Doctor and Sarah Jane is extremely heartwarming, especially since everyone else had their doubts on who he was for a few minuties, because most of them were only familiar with the Tenth Doctor not the Eleventh (or in Jo's case just the first three Doctors), expect good old Sarah Jane.
Sarah Jane: It's you, isn't it? Oh, you've done it again!
Sarah Jane eventually gets a real daughter when she adopts Sky in series 5.
Clyde's interactions with the homeless girl Ellie in "The Curse of Clyde Langer" fall somewhere between heartwarming and Tear Jerker.
Clyde's first, but brief, meeting with her - Note that this is before he is cursed - he gives her some money for a bacon sandwich because, in his eyes, being a "Scrounger" might not be her fault.
Sky, the only member of the main cast aside from Clyde himself not affected by the curse on his name, constantly works to force them to realize that their rage every time she mentions his name doesn't make any sense
The interactions between Luke and Sky in "The Man Who Never Was." Despite this being the first time they've met in person, they soon do start acting like siblings, possibly due to their similar circumstances