I find it difficult to pattern-match any of the characters to the classic hero template, especially when you compare them to traditional hero archetypes such as Green Lantern or someone like that. As I said, Dany is initially motivated by personal survival, with a dose of revenge fantasy on the side. Her actions are impressive, but hardly selfless. Her motivations do change as her character develops, at which point she begins to think in terms of social structures and armies -- again, as opposed to a more classical hero who would think in terms of beating up bad guys in person.
You are right about Jon being more of a heroic archetype, but even he ends up making several distinctly un-heroic choices that cause a lot of damage to the... well... not the "good guys", exactly; I guess you'd call them the "comparatively less bad guys".
Ned is probably the most heroic character in the entire story, which is why ur trgf xvyyrq bss engure dhvpxyl. Urebrf qba'g ynfg ybat va gur jbeyq bs NFbVnS.
Oh, and I am reasonably sure that the [quasi-]supernatural properties of any of these characters will have little, if anything, to do with their ultimate fates (other than in terms of PR). At least, this has been the pattern so far.
See also: Everything I Needed To Know About Life, I Learned From Supervillains
-- Quirinus Quirrell
-- Quirinus_Quirrell
I was once asked whether I would rather be a superhero or a supervillain, and I probably shouldn't tell you how little time it took for me to answer "supervillain."
Being a superhero sounds awful, at least if you intend to keep being recognized as a superhero. Superheroes are bound by the chains of public opinion. A superhero can only do what people generally agree is good for superheroes to do. If you stray too far off the beaten path in search of how best to use your superpowers to actually save the world, you could easily end up doing things that look, at first glance, somewhat to incredibly evil. And if people are going to turn against you once you start actually optimizing, you might as well just be a supervillain to begin with. They look like they're having more fun anyway.
You probably won't get the chance to decide between being a superhero or a supervillain, but you do get the chance to decide what kind of person you think of yourself as, and I think you should think of yourself more as a supervillain than as a superhero. Why?
In the same way that being a superhero limits what you can do, thinking of yourself as a superhero limits what you can think. And if you want to save the world, you can't afford to limit what you can think. Humanity faces many difficult problems, and the space of possible solutions to any one of these problems is large. If you have censors in your mind that are preventing you from looking at parts of this space because some of your moral intuitions don't like them ("that's not the kind of thing a superhero would do!"), you're crippling your ability to search for solutions to problems. For example, your moral intuitions are likely to flinch away from solutions to problems that involve you causing bad things to happen but be okay with solutions to problems that involve you failing to prevent bad things from happening (think of the trolley problem, or Batman's policy of not killing his enemies).
Edit (2/19): But thinking of yourself as a supervillain has the opposite effect. It's easier not to flinch at certain kinds of ideas, which now come more easily to mind and may not have otherwise occurred to you. For example, on Facebook, Eliezer recently mentioned a thread where people were posting examples of things that they valued at a billion dollars or more, such as their cats. With a supervillain module running in the background, I noticed and pointed out that this constituted a thread where people publicly described how they could be ransomed. I can't exactly test this, but I don't think this kind of idea would have occurred to me before I installed the supervillain module. (This is a tame example. I won't give less tame examples for obvious reasons.)
There are many things you can't say, but you don't have to say everything you think. Until someone discovers a technique for reliably reading human minds, think whatever thoughts best help you accomplish your goals without worrying about any moral labels they may or may not, upon reflection, ultimately warrant. Moral labels are for a later step in the decision process than the part where you generate ideas.