Criminals of any sort. From the petty shoplifters, to the mass murderers, to the politicians.
Not because I feel a great deal of empathy for them, but because it seems that few people feel any for them at all.
I'm not exactly a determinist. I think that people can make choices that can change the future. However, I think it's a little foolish to judge someone's actions as if their history didn't limit those choices. If a person is raised to believe that [insert group here] are hurting your friends and family, and that they aren't real people, then why would they bother to learn the opposite?
I try (and fail, often) to not judge anyone other than myself. For the most part, I know why I do (or don't do) things. I know the reason why I didn't say "thank you" to the bus driver is because I was exhausted, not because I was deliberately trying to be rude, and I judge myself less harshly; I know that the reason I was late is because I got distracted reading again and not because of any circumstances out of my own control, and I judge myself more harshly. With someone else's actions, I can't know that.
On my worst days, I am a smug, condescending, pretentious, destructive, intolerant asshole. I don't have days like that very often, but I've had them enough to know that that side of me exists. On the other hand, most days, I'm helpful and friendly to pretty much everyone (or, at least, I try to be; for me, "friendly" means "be pleasant when social contact is unavoidable, avoid social contact if it is polite to do so"). I would not want someone to judge who I am as a person by my worst days, and, for most people, how am I supposed to know if their behaviour is because they're a bad person, or just having a very bad day/week/month/year?
So, when someone does something horrible, I reflect that this person is human, like I am, and that somewhere in me, there's version of me that was brought up to believe that sinners are bad people who deserve eternal torture, and that whatever brief suffering I bring to them now means nothing next to that, and, if I have exactly the wrong series of really, really bad days, that part of me might come to the forefront. And that if I don't want it to happen, that that's exactly what I have to do: to think of these people as people, and not as "sinners" or "criminals" or any other label that strips them of their humanity.
If someone else chooses to see those people as monsters, then, well, I try not to judge them, either. Their choices have been just as restricted. But I do try to convince them to look at the "monsters" the same way I do. Because maybe there will be a day when they are face-to-face with some of their monsters, and my words will have given them a choice to not become a monster themselves.
On another note, I don't think that "not having sympathy/empathy" is the right concept. The very concept of schadenfreude is that you do feel the pain that the other person is feeling, you know that they're hurting, and the sympathetic pain gives you pleasure. But I can't find a better word or saying or whatever to express the concept that we're going for here, so I'll just leave it at that.