When Tracy Jordan tells a heartbreaking story about his diabetic daughter at a fundraiser. Subverted when it turns out that he doesn't have a daughter—he made it up to get donations and to get Jack in Don Geiss' good books.
In the episode "MILF Island", someone tells a newspaper reporter that Jack is a "class-A moron". Jack then tells Liz about how that insult particularly hurts his feelings: as a child, he had low self-esteem and a stutter, and he was often bullied and called a class-A moron by his peers. At the end of the episode Jack becomes so distressed about it that he starts to stutter again ("Whoever said that, they meant it. They think I'm a moron like Gilly and everyone else... It's just k-killing me that someone would say that about me... L-Liz, I g-g-guess I'll always b-b-b-be that k-k-k-k-k-k-k-k...") Liz gets so upset that she admits to being the one that told the paper that Jack was a moron. Subverted though in that Jack was making the whole thing up and was just guilting Liz into admitting she had done it.
Tracy's movie, Hard to Watch, is apparently incredibly moving.
Colleen's quiet death in a Central Park horse carriage. Jack during the entire episode thinks she's lying about dying. It isn't helped that she refuses to take an ambulance to the hospital (where her heart attack might have been prevented), but it seems at age 87 she simply felt she was holding Jack back.
The ending of A Goon's Deed in a Weary World. Just... wow.