The opening, which takes us on a tour of Rocky's rise to fame after winning the Heavyweight championship and also introduced the world to Survivor's "Eye of the Tiger".
Clubber Lang deserves mention for his rise in the ranks, and noticing that Rocky isn't fighting top contenders while attending his matches. For all his faults, Lang is a boxing prodigy.
Paulie gets about his only Awesome moment in the whole franchise when Rocky is being chokelifted by Thunderlips, and Paulie without hesitation charges in screaming and busts a folding chair over the giant's back... and then stands and faces him down to give Rocky time to regroup.
Paulie: I don't sweat you!
Granted, Thunderlips drops him with one punch, but he stood there and took it.
The charity match in general. It has nothing to do with the plot (besides foreshadowing a few things, like Mickey's heart condition), but it's a great way to get you pumped up for the rest of the movie.
After the initial training with Apollo goes south, Adrian gets an understated one that's actually rather spectacular in its own right; when she manages to get Rocky to let go and be honest with himself with a hefty verbal beatdown. It doubles as a Heartwarming Moment as proof that for all the crap that the two of have to go through, she's there fighting right next to him every time.
Rocky: How'd you get to be so tough?
Adrian: I married a fighter.
For a rare antagonist moment, despite his loss in the rematch, Clubber Lang will forever go down in Rocky movie history as the first and only boxer to ever knock Rocky Balboa out.
Rocky going through training with the additional motivation. He's gotten more mobile, faster, and not to mention, seems to move and fight a lot like Apollo. The climatic moment with the strings in "Gonna Fly Now" reaching their height when Rocky finally manages to outsprint Apollo on the beach, the sign Apollo said that he would be ready for the fight, and the Man Hug that follows at the end seals the awesomeness deal.
Stallone confirmed that this was the lightest weight he ever had in a Rocky film: 163 pounds on a 5'10" frame. For comparison, he was 178 in the first film and bulked up to 200 in Rocky II. This means in-universe, Apollo trained every bit of fat off his body so he'd be extra quick during his re-match with Clubber, who relies more on power as opposed to speed or endurance.
Throughout the entire fight, Rocky is absolutely dominating Clubber Lang. While Clubber manages to get in shots during round 2, Rocky never receives any serious damage from their fight. The first round was especially awesome because Rocky just throws out devastating punches like confetti and Clubber is just getting knocked around with no idea what's going on.
After being on the receiving end of Clubber Lang's Trash Talk and getting the stuffing beaten out of him throughout most of the film, Rocky finally returns the Trash Talk toward the end of their fight, goading him into attacking while suddenly dodging and blocking everything Lang throws at him, before knocking him out.
"C'MON! YOU AIN'T SO BAAAD!"
Not to mention how accomplished Rocky felt. He won a match without getting hurt badly, without relying on luck (as Mickey and Apollo likes to claim), and with his own wit to carry him through.
Like his real life inspiration George Foreman, Lang relied on his strength, which failed him the second he fought someone who knew how to counter it. In real life, that was Muhammad Ali, who used the Rope-A-Dope technique which just makes strength useless, but in the movie? Rocky actually took all that punishment, and it STILL wasn't enough. Without his raw power, Lang quickly fizzles out and Rocky gains the advantage.
If you pay attention, you can see Clubber Lang's team trying to revive him with smelling salts after the match. Rocky didn't just knock him down for ten seconds, he knocked him unconscious.
The ending, which was Rocky having his third fight with Apollo Creed with no TV, no newspapers, and just the two of them. We then learn later in Creed that Apollo won the fight.
Apollo: I'm still young enough to whip your butt, Stallion.
Rocky: Oh yeah? How you gonna do that? You taught me everything you know.
Apollo:Almost everything. You got to remember now, you fight great, but I'm a great fighter.
with Apollo Creed with no TV, no newspapers, and just the two of them. We then learn later in Creed that Apollo won the fight.Apollo: I'm still young enough to whip your butt, Stallion.Rocky: Oh yeah? How you gonna do that? You taught me everything you know.Apollo: Almost everything. You got to remember now, you fight great, but I'm a great fighter.