Albert's speech about being an adamant pacifist, particularly at the end when he says "I love you, Sheriff Truman."
Available here. It's one of the best moments in the show.
The scenes where Ben Horne looks back on his childhood are both heartwarming and funny.
The night Catherine comes back home to Pete in her Tajemura disguise. The look on his face when he realizes it's her made this troper crack a smile from ear to ear.
In Fire Walk With Me the final scene where a despondent Laura, trapped in the Black Lodge, is visited by the angel that she thought had abandoned her. Her sudden realisation that she was still a good person worthy of love and protection, despite the terrible experiences she had suffered, was a truly heartwarming moment.
Major Briggs telling Bobby about his vision of Bobby's future happiness.
Cooper guiding Leland into heaven, and then telling Sarah how peaceful his death was.
Cooper's would-be exit from the town, with Harry giving him a fly lure and a Bookhouse Boys badge, and his perfect sendoffs to Hawk, Andy, and Lucy.
The scene between Cooper and Audrey where she tries to seduce him is easily the most heartwarming in the series.
Many of the scenes between James and Donna can be this, especially when the latter comes to realize how much she loves him.
Cooper in general is a heartwarmingly good and loveable character. The same can be said for Garland Briggs.