Although Atticus loses the trial where he was defending Tom Robinson, one of the most moving moments in the film was near the end, when the crowd rises as Atticus exits the courtroom. Scout remains seated, and a man tells her to stand up, because "Your father's passin'."
Atticus stood for justice, for the Right of an African American to have a fair trial during a time when such Rights where routinely violated. Even in defeat, they did not forget the heroism Atticus displayed, and at least one member of the gallery wanted to impress the importance of the moment upon Scout.
I agree with enotechris that is definitely a very moving part. Some others are:
Atticus Finch's closing speech "Now, gentlemen, in this country, our courts are the great levelers. In our courts, all men are created equal. I'm no idealist to believe firmly in the integrity of our courts and of our jury system - that's no ideal to me. That is a living, working reality! Now I am confident that you gentlemen will review, without passion, the evidence that you have heard, come to a decision and restore this man to his family. In the name of GOD, do your duty. In the name of God, believe... Tom Robinson."
After they find out that Boo Radley killed Mr. Ewell (not sure about the spelling there)and Atticus was talking with Heck Tate