The end of the film, where Matt decides to honor Andrew's wishes by going to Tibet, and confirming that he really did care deeply for Andrew despite seeming to grow apart from him in high school.
Andrew comforting his mother's laboured breathing by gently rolling her over and draping the blanket over her; if you listen carefully, you can actually hear her whispering "thank you." Of course, things go south about two minutes later.
The scene with the three boys lying together and just talking after they fly for the first time, with all three of them agreeing that this has been the best day of their lives.
When Andrew's getting ready for the talent show and talking about how Steve loaned him some clothes, his mother comments how good it is that he's spending time with his friends; the fact that she goes out of her way to encourage and nurture her son even when she's virtually at death's door just makes the scene that much more heartwarming.
The way Matt refuses to believe that Andrew is a bad person. Even when Andrew goes on a Roaring Rampage of Revenge and destroys pretty much half of Seattle, Matt continues to plead with Andrew, convincing him that he is a good guy. Matt even seems genuine when he apologizes for neglecting Andrew earlier on in the film.
Matt and Steve's speeches to Andrew's camera, showing that they genuinely are his friends. As with everything else, things go south after this, but it's still a heartwarming set of moments.