Rocky not caring two bits about the judges' decision in the first and last films.
Mickey's (cranky) concern over Rocky's job as a leg-breaker in the first film - Rocky (sheepish): "It's a living." Mickey: "IT'S A WASTE OF LIFE"
The end credits of Rocky Balboa, in which we see actual videos of fans running up the stairs at the Philadelphia Museum of Art and dancing triumphantly as the theme song plays. Manly Tears were shed.
This. Just absolutely this. You've got Rocky who has just gone the distance with the Champ, surrounded by reporters asking him what he's going to do following the match, and all he cares about is her.
The moment before Rocky's fight in IV when Paulie finally goes from being a Jerkass to being a Jerk with a Heart of Gold. Words on a site don't do it justice but it'll have to do:
Paulie: "I know sometimes I act stupid and I say stupid things, but you kept me around and other people would have said "drop that bum". You give me respect. You know it's kinda hard for me to say these kinda things, cuz it ain't my way, but if I could just unzip myself and step out and be someone else, I'd wanna be you. You're all heart, Rock."
Real-Life Example / Defictionalization: The city of Philadelphia has embraced the Rocky series so much, that the statue from Rocky III actually exists outside of the Philadelphia Museum of Art. Adrian Balboa actually has a real grave in Philadelphia too, out of respect for the character. (Talia Shire is still alive and well as of this writing...)
While mostly a Tear Jerker, Rocky at Mickey's funeral reciting a Judaism prayer with the help of a Rabbi is pretty heartwarming. Rocky himself is a Devout Roman Catholic, and the fact that he respects his trainer/mentor/father figure so much that he prays in Mick's religion, just shows how much he loves Mick.