Each person has a line for what is appropriate and what isn't. And it's pretty safe to say that each person's line is a little different.What offends one person won't offend another, although they may find it tasteless. Sometimes, it's so far back in the zone of poor humor that no one finds it funny--the jerks who made jokes about the tsunami or the unrest in the Middle East have been pretty well ostracized, rightly so in my opinion.
The things that are just plain wrong are easy to see, despite the stupid some people spout. However, the things that change from person to person are really tough to determine. If I heard a joke that was incredibly sexist, I would be offended, although I might not react (depends on if the person is normally a jerk or not; if they are, then hell yeah I'd say that's offensive). If someone made a joke about kids being bullied in school, I'd most definitely react. It's one of my buttons. Even so, I wouldn't be a jerk about it because the line I have drawn around my sensitivities isn't visible to anyone else.
The question becomes, how do you react when someone tells you you've said something offensive? Me, I apologize and be more thoughtful around the person in the future. Honestly, I wouldn't stop making jokes about a subject in private with my friends. If the whole world did try not to offend anybody, then we'd end up in Harrison Bergeron land with a sterile, bland world where everyone is afraid to speak lest they hurt someone's feelings, even if that person is no where to be seen.
It's okay to be offended by things. It's okay not to tell jokes you know will hurt someone's feelings. It's okay to tell the jokes as long as you're not trying to be a jerk and hurt someone's feelings. Finally, it's not okay to expect others to not tell jokes that offend you ever. If it really is offensive, other people will (I hope) tell the person to shut up and maybe they'll start to get it.
Because we really can't force understanding on someone. Each person learns that for him/herself. And I believe that people who are actually sensitive is better than those following the rules so they don't get in trouble.