At the end of the eighth-season Second Chance episode, Lance Nitahara won the final round, but gave some of the prize money to his competitor so she could fly home to France to see her ailing grandmother. It was pretty clear nobody was expecting it.
Pretty much the entire episode where four school lunchladies competed.
The entirety of the Judges' episode of the 2nd All-Stars Tournament. Geoffrey Zakarian, Amanda Freitag, and Aaron Sanchez watching four of their fellow judges compete, and hating every single elimination, each judge hugging and congratulating the eliminated competitor.
Chris Santos' elimination might have been the most tearjerking/heartwarming. He talks about his charity, a foundation treating patients of a disease which only strikes girls (his young cousin being one such patient), bringing tears to Alex Guarnaschelli's eyes again and causing Amanda Freitag to practically vault the table to hug him.
The first one wasn't much better. It was generally happier given the bickering, but Alex, Chris, and Marc are also obviously uncomfortable judging their fellows, and Alex is close to tears when Amanda is chopped.
The teen chef episode. The judges actually declare that they can judge these teens as accomplished chefs, respect them and their passion, and in the end, all the eliminated competitors are given a $1000 dollar gift card.
The teen tournament also had another bit of heartwarming. On one of the rounds, two girls made it to the last round. As they await the results, they are holding each other's hands in support no matter which of them gets chopped.
Major feels in the "Unsung Heroes" episode. Each competitor is someone who serves their community with food (cooking for poor kids, seniors, or people at dietary risk because of illnesses). The judges even come out and say that it's hard to eliminate any of them just because they're all so admired. One chef breaks down crying when she describes her work and it's kinda tough not to join in with her. The winner gleefully does push-ups at the end of the episode.