I find it hard to empathize with things that happen a million miles away as well, it's tragic and disturbing and makes me hate the meanness people are capable of. Mostly it is the injustice which can make me pretty angry, but I feel detached about it other than that.
People I know are going out of their way to do fundraisers for Haiti, and I don't participate or donate... I never do when there is some major tragedy far away. 1) I don't have expendable income and 2) I'd be more likely to give it to someone close to me who is also in need... leave the donating to the rich folks (well, rich compared to me, lol).
I think generally, I do have empathy, but more as a learned behavior, especially with people close to me. You say you're sorry, you try to relate, try to think of saying things that might help even if they don't, I often say expected things because that is how I was raised, it is automatic and is suppose to make the other feel better. And if I don't, then I feel like a jerk. Often times I'd just prefer to just give them a hug, tell them I love them, and let them be, because I don't really know what to do/say, but I should say/do something.
Sometimes, my lack of empathy makes me feel like I'm not nice enough, but like Chimera said, you cannot empathize with everything or you'd go mad and die from lack of care for yourself.
It is no different in the animal kingdom, humans may have more empathy for animals due to their helplessness or human's injustices done to them and I totally understand that, but at the same time, the animal kingdom is filled with as much unfair, mean crap as ours is.. weaker animals are prey and stronger animals do as they please.
I do have empathy for children and old people. Old people mostly because they are completely dependent and their bodies are falling apart and failing them, meanwhile their children have to become their caretakers and you lose your freedoms. That would be horrid.