From the original, one throw-away line during the "help the penguins" montage near the climax:
"I do not want to live in a world without Penguins!"
In the sequel, the entire scene where Gloria sings "Bridge of Light" to Erik. It gets better when the other penguins join in.
It gets more Heartwarming at the end when Erik joins in.
Erik singing an improvised opera about how heroic and brave his father is to convince the elephant seals to help the penguins, and it works.
Everyone trying to help each other out from being trapped to the song Under Pressure.
Even the penguins who are trapped help by singing and encouraging the penguins and elephant seals who are pounding on the ice.
Gloria tears up when Erik starts singing along with her.
Creatures of the world unite...
Erik dancing on Mumble's feet near the beginning. Sure, it goes wrong less than a minute later, but the sheer joy on his face is wonderful to see.
In the first film, the Amigos just accept Mumble as one of their own, no questions asked, and they stick by him all through both films. Fast and true friends, indeed.
In the first movie, the slow, building scene after it looks like Gloria is rejecting Mumble for the final time... and then in desperation he finally stops trying to be pretending to be something he's not and begins to dance without holding back... and they both realize that his rhythm matches Gloria's heartsong.
Later, when Mumble's party is on their way to find the aliens, Gloria arrives, and begins serenading Mumble, fully prepared to go with him to the ends of the earth, having realized her love for him. Mumble protests, stating that she may lose her friends, family, everything she cares about on their journey — and Gloria simply responds, "Then I'll have you." Mumble is still determined to send her away, but is visibly moved and elated that Gloria is reciprocating his love.
When Mumble finally succeeds in driving Gloria away so she won't be endangered by their quest, the Amigos assure Mumble that he did a very brave, noble thing.
During the final push on their journey, the group is pushing through an almighty blizzard. They're constantly getting pushed back, but once they all finally unite and push together as one, they are able to push through.
Ramon finally winning Carmen's heart off by leaping off the doomberg to join her in the blocked-off Emperorland.
Ramon: A thousand lifetimes up there is nothing to this one exquisite moment by your side.
The aliens/human expedition team dancing with the penguins in the first film.
Bryan's breathless, overjoyed "Boys..." upon seeing his pups again, after Mumble saves him from the ice crevice.
Sven reassuring Erik that he believes in him, and giving him the "if you want it, you must will it; if you will it, it will be yours" mantra. And receiving a big hug in return.
Another one is the little remark he makes after learning of Erik's name.
Sven: Erik. In my homeland, we have many brave warriors named Erik.
Really, Sven and Erik's entire friendship. Erik absolutely adores Sven, and is never once shown losing too much faith in him, even when he learns that Sven is not a penguin. Sven—given his personality—can easily be mistaken for just enjoying the adoration he gets from the child, but even after he reveals what he is, he still shows genuine concern for Erik, and his encouragement was proved sincere. When Erik nearly fell off of the glacier, Sven reacted in absolute horror and was ready to save him, unafraid to show his face again if it meant helping the young penguin.
Sven:(to himself) Erik...(flies towards his friend) Hold on Erik, I'm on my way!