There are too many examples to count but Lieutenant Dan finding peace is among the best. It's also when he finally moves to First-Name Basis with Forrest.
Lieutenant Dan: Forrest, I never thanked you for saving my life. Forrest (voiceover): He never actually said so, but I think he made his peace with God.
This is especially true when you consider that, earlier in the film, Lieutenant Dan was a Death Seeker who wanted to die heroically in battle, and he was furious with Forrest for saving his life.
And when Lt. Dan shows up at Forrest and Jenny's wedding, with "Magic Legs"and a Vietnamese fiancee of his own.
"You know it's funny what a young man recollects? 'Cause I don't remember bein' born. I don't recall what I got for my first Christmas and I don't know when I went on my first outdoor picnic. But I do remember the first time I heard the sweetest voice in the wide world."
Young Jenny: You can sit here if ya want.
Forrest tells his story to an old woman. He realizes she just missed her bus, and he tells her so. Her response?
Old Woman:[crying, smiling] There'll be another one shortly.
The old woman is the fourth person Forrest spoke to. The first one, a younger woman, initially didn't appear too interested to listen and just let Forrest talk while she read. By the time her bus arrived, she was listening intently to his story.
Early before that while Lieutenant Dan was being bitter at being rescued he still had Forrest's back in 'Nam; after Forrest got shot, what does Dan do? He fires back at the shooter screaming and taunting them while Forrest drags him to the safe zone.
As well, as Forrest's direct commanding officer, he would have had to support Forrest's Medal of Honor application.
Forrest sending part of the profits from his shrimping business to Bubba's mother, ensuring that she can live an easy life.
Even better when you realized that it was a promise he made to the, at that point, dead Bubba.
It's a small detail but seeing Bubba's mother and siblings at Forrest and Jenny's wedding (they sit in the second and third rows on the left).
Forrest and Jenny reunite at an anti-war rally at the Lincoln Memorial, with hundreds of hippies cheering. Sappy? Maybe. Adorable? Absolutely.
Forrest tells Jenny about his experiences when she is on her death bed. He talks about the beauty of nature of the places he went. The sunsets at home, the rainforests of Vietnam, the mountain range during his cross-country run that looked like two skies piled on top of the other, etc. He just breaks down crying when he gets to the end.
In one of the most tender Puppy Love moments you'll see, young Jenny sneaks away to Forrest's house when the weather outside scares her and sleeps in an embrace next to him.
During George Wallace's Stand at the Schoolhouse Door event, Forrest went to pick up and return a notebook dropped by Vivian Malone Jones, one of the black students going to register, completely unaware of the situation around him and what he did. To Forrest Gump, "racism" isn't even a word.
Overlaps with awesome, but when young Forrest's leg braces shatter and he is able to really run for the first time, the look on his face is almost as if to say "Oh, HELL YES!!"
When Forrest first sees his son, he asks Jenny if he's like him, showing Forrest has an awareness of his intellectual disability, the face he makes upon finding out he is exceptional is both heartwarming and a tearjerker, what makes this worse is this is right before Jenny tells Forrest she's terminally ill
Forrest: He's the most beautiful thing I've ever seen but is he smart or is he— (Places hand on chest)... Jenny: He's very smart. He's one of the smartest in his class.
Jenny names her son with Forrest Forrest Jr.. She didn't want to marry him (at first), but she did love Forrest enough to name her son after him. Hell, just the fact that Forrest and Jenny even have a son, considering what each of them went through before they got to that point.
Notice that Forrest at first assumes that Junior isn't his, and shows nothing but support and happiness that Jenny had a child with someone else.
Doubles as a Brick Joke: When Forrest tells Dorothy Harris that they aren't strangers any more, Dorothy gives him a big smile. 30 years later, she does the same with Forrest Jr. when he introduces himself.
Forrest's reason for going into the shrimping business even after Bubba was long dead: he made a promise and said he fully intended to keep any promise he made, even if it included telling a little white lie about not preferring his personal ping pong paddle to earn some sponsorship money to buy a boat with.
The reason Forrest took the actions that ended up getting him the Medal of Honor: He wasn't trying to be brave, he was just trying to find Bubba. Every time he came across another soldier wounded in the ambush, he'd pick him up and take him to safety, because Forrest is a decent person and it was the decent thing to do.
The ending of the movie, where Forrest sends his son off to school, having lived a very fulfilling and eventful life (which is by no means over), being an extremely successful business owner...and with a son who loves him.