Rufus's flashback to when he last saw Penny, alone on her bed, sad because she wasn't adopted, and comforts her with his "Faith is a Bluebird" poem. The music that plays in this scene is also tear jerking. As is Penny saying "I love you, Rufus" while petting the grandfatherly cat.
If 'Faith is a Bluebird' doesn't make you tear up a little, you are not human.
Faith is a bluebird you see from afar.
It's for real, and as true as the first evening star.
You can't touch it, or buy it, or wrap it up tight;
But it's there just the same, making things turn out right.
The "Tomorrow is Another Day" montage.
Miss Bianca cuddling up with Bernard on their way to Louisiana.
Penny praying, not only for herself, but for her teddy, Rufus, and all the kids at her orphanage, and that she and they will all find happy homes and be adopted by new families.
The entirety of 'Someone's Waiting For You'. Some of the most gorgeous lyrics ever; not even necessarily the most poetic, but beautiful in their simplicity, and sung with an incredible amount of emotion.
Be brave, little one... make a wish for each sad little tear... hold your head up, though no one is near; someone's waiting for you...
The Rescuers Down Under
Marahute thanks Cody by taking him on the ride of his life, and gives him a feather.
Before that, when Marahute shows Cody her nest and he asks if they're due to hatch soon, she coos and fluffs up her feathers. Without uttering a single word, it's apparent that she's quite happy.
Cody is kidnapped by McLeach and the boy is dragged away with no other human knowing what has happened and no help will ever come. However, one mouse begs to differ as he rushes to a mouse radio transmission station to start a message relay to New York City to alert the Rescue Aid Society. In this sequence, you see a whole network of mice who have dedicated their lives to ensure that for the forgotten and oppressed, help is on the way.
See the scene here. The heartwarming turns funny when you realize that the Rescue Aid Society has absolutely no problem with usurping proper channels to get their message through. Who cares if dozens of humans are confused at all of these "R.A.S"'s popping up on their screens if a child can be helped?
Wilbur initially refuses to fly Bernard and Bianca to Australia (or anywhere) due to the massive blizzard outside. The moment they confirm that a child has been kidnapped and they're on a rescue mission? He's ready to fly!
Bianca: Oh, Cody, you mustn't give up hope. Bernard is still out there.
Jake: That's right. If there's anyone that can bail us out of this scrape, it's old Bernard. (surreptitiously) Nice bluff, Miss B.
Even more heartwarming when connected to the first film. Bianca has always believed that Bernard is capable of more than others (including Bernard himself) think he is, and he's always lived up to her expectations.
At the end, when Bernard finally manages the speech he's been working up to the whole movie: "Miss Bianca, before anything else happens ... will you marry me?"