Historian
I think prejudice is a matter of feeling; it's a hostile or dismissive attitude, a feeling toward people we find different from ourselves in some way, and some way that we take as significant, but racism is more than that. Racism is a whole set of beliefs about that which justifies those feelings and tries to make the case for differences that we find are innate, permanent, and are the basis for action, the basis for discrimination, or even for an institution that will be based on these ...
Social Anthropologist
I think that prejudice is a general statement; it's a general attitude or general belief system about anything, and it comes out of not investigating the facts and now knowing the true nature of whatever that thing is that you're prejudiced against. Racism is a particular kind of prejudice against other human beings, or groups of human beings, and it's usually irrational, and as George says, it's based on the assumption that there are inequalities among the races.
Historian
I would agree with George and Audrey, and add that prejudice can apply to lots of things, not only race. But racism is based on the assumption that race is an indicator of basic traits of character. That is, if you know a person's race, you can say a lot more than simply what race the person is. Presumably, you can say how the person might think, how the person might react, his inclination, his physical abilities, all those kinds of things. And of course, you can't do anything about your...