There's always going to be a certain amount of subjectivity to this kind of thing. Different people react differently and all that. But in general I think the answer is well-conveyed emotions combined with empathy. You have to *know* what the character in question is going through, and you need to connect to them.
That's why I think comics (and cartoons) are a good medium for it, to some extent. The characters are (usually) very broad and obvious, with comparatively little subtlety to them. And I mean the characters themselves, not necessarily the stories. It's a consequence of the way comics (and cartoons) tend to work. You have to build up the characters over a fairly short span or time, with few pages/panels to get the job done. So you have to break the characters down to their basic characteristics and get them across as quickly and well as you can.
That's a real boon here, though, because it makes it so easy to 'get' the character. You can understand them in a very short period of time, ideally without ever feeling that there's anything lacking. The art helps a lot there, because it's (again) so easy to understand the expression on a well-drawn character's face.
So you end up with very easy-to-understand characters with very obvious emotions, and not a lot of clutter to get in the way. It's very... clean, and very direct, which really works for a lot of people.
I mean, take the Iron Giant, or Dinobot. They're both characters without a lot to them, and not remotely in a bad way. Think about it. How hard is it to determine what their reactions would be in any given situation? Pretty easy. So seeing them in a tragic situation has a sort of purity to it. Nothing in the way. It lets you focus on the moment and completely *get* it.