I can't say as I get offended all that much, but then again, I've always felt that I have pretty thick skin. I probably get second-hand offended at what people say more than anything, especially behind someone else's back. I'm not the kind that likes to get into confrontations, but if you're going to say something about someone that you wouldn't say to their face, then don't say it at all.
As for anything racist, I always just shake my head when someone makes a remark. Nothing makes you better than someone else because of your race/ethnicity, but I'm not going to get in a war of words with someone if their opinion's already ingrained into them (it always seems to come from older folks in their 50s+).