The moment when Kevin Costner's father's ghost comes walking into the diamond - and you realize what all this has really been about.
Ray having time-traveled back to 1972 tries to convince Doc Graham to come with him back to Iowa to fulfill his dream of getting a hit in a major league game. Graham, however, refuses to go:
Ray: Fifty years ago, for five minutes you came within... you... you came this close. It would kill some men to get so close to their dream and not touch it. God, they'd consider it a tragedy. Doc Graham: Son, if I'd only gotten to be a doctor for five minutes, now thatwould have been a tragedy.
Mann, trying to find out why The Voice sent him and Ray to find "Moonlight" Graham, interviews the residents of Chisholm who knew Doc, and they tell all these fantastic stories of a decent, warm, cheerful guy who took care of the city for over 50 years.
The moment when Archie Graham steps out of the diamond to save Karin. Being "Moonlight Graham" was his dream, but being "Doctor Graham" was his life. And when a little girl was in danger, he chose which one he needed to be more. Even if it meant he couldn't go back.
The scene when all the baseball players say goodbye to Moonlight Graham, after he steps over the threshold to save Karin's life.
Shoeless Joe: Hey, rookie!
(The elderly Moonlight looks over at Joe)
Shoeless Joe: ...you were good.
(Moonlight offers a wistful, bittersweet smile before stepping into the cornfield for the last time)
What makes the scene poignant is that (1) they're respecting him as "Doc", the man who saved Karin's life, rather than as "Moonlight", and (2) it was Burt Lancaster's final role.
When Terrence Mann follows the players into the cornfield, he starts giggling like a young child again, and you realize that he's finally found peace. He also states that he'll do something he hadn't done in 20 years: write a book ("Shoeless Joe Comes To Iowa").
On a meta level, this movie is a Heartwarming love letter to baseball itself.