I have trouble with empathy as an emotion, but I am gaining a grasp on it intellectually (I know when I should feel empathy). Books have helped enormously. A year and a half ago I read Night and had an epiphany of sorts- I understood that caring for others, in large or small situations, is important. I felt bad that Elie Wiesel's father died of dysentery in Buchenwald, and I understood that not feeling bad about this would be quite abnormal.
I feel empathy readily for my mother and people in books, see, but I tend to lose it around other, breathing humans. Sometimes I just do not have the energy to care about people's issues. I grow especially weary of people's love problems. However, I am A LOT better about this than I used to be.
People who have struggles with empathy might find Holocaust literature very helpful.
These books contain valuable emotional engagement and enough historical trivia to keep an aspie interested.