Lt. Dan, legless, up in the rigging on top of the shrimp boat, in front of a wildly waving American flag, shouting at Hurricane Carmen and God Himself to dare and sink that boat. Not the crowning moment he set out to have back in Vietnam, but it's enough. Then, a few minutes of screen time later, he casually goes for a swim in the Gulf of Mexico.
Forrest, at least, considers the swim to be the awesome part.
Forrest's Crowning Moment of Awesome would almost certainly have to be when he breaks out of his leg braces, and runs for the first time.
Let's also not forget the scene where Forrest, in Vietnam, runs repeatedly into the jungle looking for Bubba, pulling out people as he goes, and then after finally finding Bubba, runs out while napalm explodesall around them.
Any scene for which someone wins a Medal of Honor, fictional or otherwise, is by definition a CMoA.
Prior to that, for someone as dumb as Forrest he does show some badass moments when during the ambush, as he was seen as one of the men firing back.
Maybe not as impressive, but enough to make you go "YES!" Mrs. Blue, who comes from a long line of servants and slaves, receiving Bubba's share of the money and moving to Florida condo. With a white housekeeper.
"And y'know what? She didn't have to work in nobody's kitchen no more."
Whenever Forrest shapes history, from Elvis's controversial hip shaking to giving John Lennon the inspiration for "Imagine".
Forrest and Jenny reuniting in the reflecting pool between the Lincoln Memorial and the Washington Monument is obviously a Crowning Moment of Heartwarming, but the image of a crowd of thousands cheering wildly for two people running to each other in waist-deep water, hugging after years of separation ... wow-ee.
Even made more awesome when the anti-war Hippies applaud their reunion (while Forrest is still dressed in full Army regalia).
Matched if not topped by Forrest catching sight of Jenny's hippie boyfriend slapping her in the face at the Black Panther "party" and running over, doing a full-body tackle and beating the shit of the little creep.
Coach Bear Bryant's line after Forrest scores a touchdown....and after knocking down the marching band.
Bryant: He must be the stupidest son of a bitch alive, but he sure is fast. HAHAHAHA!!!!
Fictional or not, anyone receiving that kind of praise from one of the greatest football coaches of all time is quite an accomplishment.
At the end, despite his Innocent Inaccurate understanding of Jenny's past, he orders her abusive father's house to be bulldozed. It really goes to show how much he respects her, even when he doesn't entirely understand what's going on.
Forrest deciding on a whim to just start running, and not stopping for three years.