In the wake of Spider-Man 2 this seems a common theme, so I thought I'd try my hand at a first attempt on it.
What is the heart of the ethics of superheroes? It is the notion of a Calling (sometimes it goes by other names, e.g., freely-chosen Destiny). One of the more insightful posts I have seen on the ethics of Spider-Man 2 is found here at "Catholic Ragemonkey," because the author, Fr. Shane Tharp, rightly touches on this point. To be a superhero is to be called to live a life apart in the service of higher things (in particular, the saving of others).
This touches, it must be said, on an important increase in ethical maturity from Spider-Man to Spider-Man 2. A line from the first movie, "With great power comes great responsibility," is often quoted. What is not often noticed is that in S2, Parker outgrows seeing his life as Spider-Man in these terms. His new maturity doesn't show it to be false; what it shows is that the principle on its own simply does not capture the full ethical situation of the superhero. It is one facet only. Were the principle all there was to it, one could circumvent it by setting aside the power. But Parker finds that when he tries to do so, he in a sense sinks below himself; indeed, at his low point he even fails to rise to the level of heroism for which we could hope in an ordinary man, just turning away when someone right in front of him needed help.
Note, too, that the ethics of a superhero is in a sense highly individualized, and in a sense something in which we all participate. There is a hero in all of us, as S2 notes; there is a sense in which we are all called to be heroes. But we are not all called to be Spider-Man; only Peter Parker is. We can say to Peter Parker, "You are called to be good, Peter; indeed, you are called to be heroically good," but no one can demand of Peter Parker that he be Spider-Man, anymore than anyone can demand of an excellent firefighter or cop that he continue in that profession. But some people are called to this; and it is to their own Conscience that they are beholden. There is no general law written on the tablet of the heart saying, Thou shalt use thy superpowers for vigilante justice," in terms of which we can say, if Peter decides no longer to be Spider-Man, "Peter, you are being immoral; turn from your wicked ways." We can appeal, we can plead, we can hope, but we cannot demand. And likewise, in the ethics of superheroes, common, ordinary people are called to be heroes; but we cannot say, "We demand of you that you following your calling." What we can do is encourage people to do so - in part, by showing them the example of the ones who do. It seems to me that the ethics of superheroes places an immense amount of importance on Conscience. What, really, can oblige Peter Parker to be Spider-Man? Conscience, alone. The ethics of superheroes is an ethics not of rules or formalized duties or consequentialist calculations; it is an ethics of conscience. There is no pre-existing general set of rules for what one should do in the particular case of having superpowers. There is only ordinary morality, and the authority of conscience in guiding us, given the very particular issues of our own situation. The morality of the superhero is ordinary morality made extraordinary by a particularized call of conscience, appropriate to the unique details of this particular case. There is a commonality, that can be demanded of everyone; but there is also a particular call, that could never be the same for any two people.
One of the great moments of S2 is in the subway train just before Spider-Man is taken, when ordinary people take a stand against a villain far exceeding their abilities to control. This is exactly the sort of thing which the ethics of superheroes calls us. We are, paradoxically, not called to a level commensurate with our abilities; we are called to a level commensurate with the need of others, even if it so far exceeds our powers that we fail. This is the level of the heroic, that it concerns itself not merely with thinking about its own responsibilities but goes beyond them to think about what is really needed. It is in this sense that being heroic is supererogatory. People are called to be heroes; but none of us are in the position to demand the heroic of others. At best we may demand it of ourselves, and plead and hope for it in others. In general, it is difficult even to demand it of ourselves.
What Peter Parker learns about being Spider-Man in S2 is that there is more at stake than his own powers, more at stake even than the responsibilities required by those powers; at stake are bigger things than anything to do with himself alone. He cannot genuinely fulfill his destiny as Spider-Man if he is concerned only with his guilt for his uncle's death. He has to forget himself. This is one of the reasons why Spider-Man is so likable. He is one of those superheroes who tends to go against villains who are, in their own ways, more powerful than he is. But he does so anyway, because it doesn't matter that he's likely to lose; what matters is that people need saving, and he is the one called to save them. Recognizing the responsibilities power brings is one step in being a superhero; but the responsibilities required by our powers are all responsibilities having to do with our use of those powers. A superhero must go beyond this, and recognize that this is only one aspect of his destiny; that the salvation of others is an entirely bigger thing than anything to do with him alone. The responsibilities are still there, but they are seen in the light of something even bigger. (I'm sometimes inclined to think we over-extend this term 'responsibility'; it indicates something of immense importance. But there are many cases to which conscience calls us where saying that we had a responsibility to do what we did is not quite right. Our responsibilities for others, and over others, are really quite limited, for instance; but what is right for us to do with respect to others is much less so. One could use 'responsibility' for this, too; but I think it's a different enough that we are running the risk of equivocation by extending the word 'responsibility' to cover this as well, particularly given how much it already covers.)