Nothing ever. I laugh at plenty of horrible things, but I never feel bad for it. Why should I, they didn't happen to me (and even then I can make fun of it).
Life is already grim (all those awful terrible things prove it, no?), why add to it by being all gloomy and sadface about it?
AS LONG as you still know the importance/significance/seriousness behind it. 9/11 was, and continues to be, a great source for humor. Just don't rofl during the opening ceremony of Freedom Tower. I've merely walked past Ground Zero as a dirty tourist and didn't feel like giggling. Picture on the internet though - they make my day. That doesn't make me a horrible person... at least not by default.
Would I get in trouble here if I posted a Dead Baby Joke?