There are many examples of bravery throughout the book by many characters, but very often we see the bravest acts performed by Atticus.
Here are just a few:
In Ch. 10 Atticus is forced to shoot a rabid dog that is coming down the street toward everyone. This is brave not only because he is facing off with the dog and no one else is, but he addresses and resolves the dangerous situation for everyone.
In Ch. 15 Atticus bravely goes to sit outside of the Macomb County jail overnight to make sure that no one hurts Tom. His concerns are warranted, as it turns out, because a group of men wanting to come in and do Tom harm show up. Atticus stands his ground.
Throughout the book Atticus shows bravery by representing Tom Robinson. Despite Tom being innocent of rape, it is a forgone conclusion that he will be convicted simply because he is black and Mayella Ewell is white. There are many people in town who would like to see Tom convicted and the trial brings a lot of tension to the surface. It is clear that Tom's life and even Atticus's life could be in danger, but Atticus still represents Tom to the best of his ability because it is "the right thing to do."