What are some examples of racial prejudice in the book?

It’s helpful to remember that prejudice means to pre-judge something or someone based upon your beliefs about them or their entire group. All of us, if honest, have prejudices that we have built up over the course of our lives, whether they were explicitly taught or simply absorbed from our experiences.
Aunt Alexandra, for example, believes that black people are gossips, so you must be careful about what you say in front of your household help. We see this at breakfast in chapter fifteen. Atticus makes a comment about how Braxton Underwood despises “Negroes” while Calpurnia is pouring Aunt Alexandra more coffee. Alexandra chides him for this bad habit, saying that “It encourages them. You know how they talk among themselves. Everything that happens in this town’s out to the Quarters before sundown.” We know from previous chapters what a great irony this is, as Aunt Alexandra herself talks about the members of the town and does her best to know about their business. That she judges black people for something she routinely engages in is a double standard and a clear example of racial prejudice.
Lee, Harper. To Kill a Mockingbird. (Soft Cover). Perennial, 1961.

The outcome of the Tom Robinson trial is the clearest example of racial prejudice in the novel. Tom Robinson is a black man living in the segregated society of Maycomb, Alabama, in the 1930s. Despite the lack of evidence, Tom's obvious handicap, and the conflicting testimonies of Bob and Mayella Ewell, Tom Robinson becomes a victim of racial injustice after he is wrongly convicted of assaulting and raping Mayella. Tom Robinson was wrongly convicted simply because he was a black man, which reveals the racist nature of Maycomb's community.
Another example of racial prejudice can be found in chapter 25, when Scout describes the prejudiced community's reaction to Tom Robinson's death. Scout recalls the townspeople saying,

To Maycomb, Tom’s death was typical. Typical of a nigger to cut and run. Typical of a nigger’s mentality to have no plan, no thought for the future, just run blind first chance he saw. . . . You know how they are. Easy come, easy go. Just shows you, that Robinson boy was legally married, they say he kept himself clean, went to church and all that, but when it comes down to the line the veneer’s mighty thin. Nigger always comes out in ‘em. (Lee, 244).