Later, when Marty goes back to help Alex. Alex feels so ashamed of trying to kill Marty that he's built a cage for himself, to protect his friends. Then there's the looks on his (and Marty's) face when he says "I don't wanna hurt you."
And after that when Alex hides in his hut, Marty just comes into the cage and says, "Alex, I ain't leaving without you."
From the Second Film
The entire opening. As a cub, Alex is captured by poachers and his father, Zuba, desperately tries to save him, then the crate Alex is trapped in gets knocked into a river, and he desperately cries for his father.
Later when the watering hole dries up, King Julien manages to convince the animals of the reserve that a volcanic sacrifice to the water gods is needed to bring it back, and Melman offers himself, and tells Gloria that he's already dying when the other animals carry him off the volcano. The look on her face when she hears this is absolutely heartbreaking.
Gloria: "This is crazy. I had to go halfway around the world to find out the perfect guy for me lived right next door."
From the Third Film
On a related note to the Gloria/Melman plot from the second movie:
Vitaly's backstory. It's no wonder why he's a Broken Ace.
His PTSD, and especially his lonely moment in his train car when he looks at the hoops and flashes back to the fire he now fears is particularly heart-wrenching.
The Third Act Misunderstanding where the circus animals learn the truth about the Zoosters. Stefano's comment about his tears being real but "you are not", what could have been Narmful, is instead quite painful. And the sheer betrayal in Gia's voice, and on both her face and Vitaly's, is even more so.
The Zoosters' return to the zoo, only to realize that they were happier with the circus and free after all while the primary trio of the circus realize that despite the earlier deception, they still dearly love their zoo friends, feel incomplete without them, and are ready to forgive them
Alex's desperate attempt to fix the plane after it broke the second time, only to come to face the fact that it's broken beyond repair. Him saying that the gang will never make it to New York really sells it, though.
The fight between Sonya and Julien. Quite the Tear Jerker, even though Sonya isn't a Funny Animal like the rest of the cast and only "speaks" in growls and grunts.