Nadia using her last ounce of strength to push Roshan over to Manny in hopes that he will be saved.
When Sid and Manny turn back to her after they take Roshan, she's gone. Nowhere to be found at all. It's pretty clear she was washed away by the river.
The Art ShiftFlashback in the cave that reveals Manny's Dark and Troubled Past. Even Diego has tears in his eyes at that scene. This is often undoubtedly considered the saddest moment in the Ice Age series.
The scene ends with a heartfelt moment between Roshan and Manny, as Manny lifts the baby up in his trunk and Roshan hugs him with tears in his eyes.
Diego taking the mortal blow for Manny during the battle with Soto at the end to protect him, as it is obvious that Soto's incisors slashed him fatally, and let's not forget that blow to his head that he got. And as he dies (the commentary for the first film confirms that he actually did die in that scene) he selflessly insists that Manny and Sid forget about him, since he wants to make sure Roshan gets home as much as they do now. This scene is especially heartbreaking if you remember that Manny has only recently lost his family, and now he is losing someone close to him all over again. His brimming eyes as he watches the dying saber only serve to drive the point home.
The scene when Runar realizes that his dog can no longer track his family's scent and that they have most likely been lost. Surely he killed most of Diego's pack, but watching him actually give up hope on ever seeing Nadia or Roshan again is so damn sad. The fact that it's silent surely hits you close to home.
When Manny and Runar look into each other's eyes after Roshan is reunited with his father. This is when Manny realizes that there is some good in humans after all, even after all they did to him.
Manny, Sid and Diego saying goodbye to Roshan is pretty heartwarming, but also Harsher in Hindsight on a meta level since the filmmakers never really thought of bringing Roshan back for anything. Especially when Manny tells him "We won't forget about you."
The score for this film really falls into this if need be. Even just by themselves, they can easily drive someone to tears. Just take a listen and prepare tissues.