Funny Moments: Several, but the first would probably be the unveiling of Akane's inner Star Wars geek when Ranma beats up the Martial Arts Sci-Fi club for her and she pockets one of their toy lightsabers.
Ranma and Akane learning that Tatewaki and Kodachi are brother and sister.
Chapter 14 Training Montage with Donny Osmond, complete with musical numbers, PLURAL. And one of them is the famous montage song from South Park!
Chapter 21 is a crowning CHAPTER of funny!
After Ranma uses the Yuujin Bakuha on him, Ryoga gets back up and it looks like he's going to throw all of his emotional weight into the Shin Shishi Hokodan...and then he gets wiped out by the Yukari-mobile and spirited away by the core cast of Azumanga Daioh to a shotgun wedding with Ayumu. The only reason it's not a flat-out Ass Pull is because of all the times Ryoga mentioned getting lost and ending up in Osaka...
After Akane's pregnancy scare, Ranma admits that part of him would have been happy to be a father.
The first time Ranma uses the Yuujin Bakuha counts as this, since it is literally powered by his love for Akane. For bonus points, comparing its power to that of Ryoga's Shishi Hokodan proves objectively that his love for Akane is more powerful than Ryoga's hatered for him. The fact that Ranma figured out how to focus his love into a Kamehame Hadoken without feeling embarrassed only makes it all the better. What really seals it as this is what Ranma says just before unleashing it all over Ryoga:
"This is the real deal, the kind that a guy like me doesn't even have the balls to declare out loud because it's just embarrassing," Ranma admitted. "But that's fine, I was always better at showing how I feel than telling!"
Magnificent Bitch: Kaori is this, as she's the one who manipulated Mousse and Gosunkugi.
Moment of Awesome: Ranma calling out (and subsequently trashing) Kuno for not defending Akane's honor after Kodachi called her several very offensive names despite his supposed love for her.
Akane gets one when she beats Kodachi... with a ZA WARUDO impression. OUCH.
Genma has one by convincing Akane to train in the Umisenken
Kasumi whupping Shampoo's ass in Chapter 16. This is even more awesome by the fact that in the previous chapter, Akane, Ryoga, Kodachi, Mousse, and Kuno teamed up had tried and failed to best Shampoo.
The way Ranma beats Ryoga after the latter learns the Shishi Hokodan. After understanding how Ryoga was using it despite not being miserable, he realized he could do the same thing using an emotional energy supply that dwarfed anything Ryoga had: His love for Akane, which also makes this something of a heartwarmer.
The final battle for Ranma plays out as an epic knockdown, drag-out fight where the previously implacable Shampoo is brought low, her guns destroyed, armor smashed and she's bleeding profusely. And as it moves to the epic crescendo of what should be the moment of triumph, Shampoo turns the tables on Akane with the Hiryu Shoten Ha. After all that, the training, the montage and everything, Akane loses. It just... goddamnit all.
Kasumi's flashbacks throughout the Sino-Japanese War Story Arc.
Akane's talk with Kasumi after she lost is one big moment where you'll keep finding something in your eye as she breaks down exactly what she has lost by losing to Shampoo.
Troll Fic: The entire point of the story for some people. On how many levels (if any at all) depends on how highly you think of the author, but various options are listed in the talk page.