I find the humor in everything, including things that other people consider crass or tasteless. It's my way of coping with the horrors of the world. However, there is a time and a place for these sort of things, and people should understand that they must live with the consequences if their humor is ill-received. For example, many people enjoyed my terrible pun in the thread about the boy who murdered that girl who turned him down for prom. I made the joke, as I said, because my way of coping with the myriad tragedies of human existence is to make jokes. However, I made that joke in an online thread containing a link to the article. I wouldn't make the joke to the parents of the innocent girl who was killed, because that would be awful. There are always going to be people who are offended by jokes about murder, or suicide, or dead babies, or anything else. If they are offended because they are offended, I just say "tough". That's life. People joke about terrible things as a way of not going insane with grief about the state of humanity.
On the other hand, if someone is offended because they have a personal experience relating to the subject matter, I will apologize for offending them and move along. I also wouldn't make the joke in the first place if I was already aware of their experiences.
I feel the same about celebrities who make tasteless jokes. I remember Gilbert Gottfried was fired from AFLAC because of some shitty jokes he made on Twitter following the Japanese tsunami. While I wasn't offended, many people were because they condemn that sort of humor. While I have no problem with it, I recognize that actions have consequences and he would have known that. I wouldn't have fired him, but given the public perception of tasteless jokes, I can see why AFLAC made that choice.
I also believe that the tasteless humor defense does not apply when you are clearly using that to (unsuccessfully) mask true bigotry, such as when celebrities or politicians or even regular people make horrifically bigoted 'jokes' about race or religion or sexual orientation or gender. There is a huge difference between, say, a waiter making a joke about black people not tipping well, and that same waiter making a similar joke while cursing, using the n-word, and following it up with "don't worry, just kidding".
And lastly, while I know it is somewhat hypocritical, the one thing I never joke about is rape. For many reasons, though I know and have heard rape jokes that would be considered funny, I don't tell them, especially in comment threads attached to articles about rape. I have made jokes about murder, suicide, terrorism, child abuse...but I just can't bring myself to joke about rape.