[Note: I don't know much about comics, so to say I'm writing this in a state of ignorance is to put it very, very mildly.]
A few days ago, while cycling home in the dark, I had an insight about Spider-man: outside of his ability to climb walls, his 'spider sense' and his 'proportional strength of a spider', there's nothing spider-like about him at all. He doesn't have the appetites of a spider - he doesn't suck carcasses dry and he only ever wraps people up in order to leave them for the police. In other words, he got all the physical benefits of being a spider, without contracting any essential 'spiderness' from his radioactive spider-bite. In contrast, think of the werewolf: werewolves (who also gain their powers through a bite) become 'wolf-like' according to a very particular understanding of what it means to be a wolf (an understanding that comes from the perspective of potential prey). So, werewolves are overcome by an urge to hunt and kill.
My initial feeling about this (and I say this as a fan of spider-man) was that this lack of 'spider-ness' meant a loss of depth to the character - I was thinking of fairy tales, archetypes, shamans with animal masks (bear in mind that I was on a bike, it was cold and wet, and I was tired). But when I thought about it a bit more, it struck me that it was a very liberating (and liberal) approach to superpowers - Peter Parker doesn't develop an essential spiderness because there is no essential spiderness - a spider in an American horror film means one thing, and I tend to think that this is, universally, what spiders mean. But Anansi, the trickster spider of Ashanti mythology, is very different. If spider-man can be described as having established a mythology, it seems to me that fundamental to that mythology is the assumption that it's not how you were born (or what you were bitten by) that matters, it's what you choose to do with your life (and I don't think it's entirely coincidental that the ever-cantankerous editor with a heart of gold Jonah Jameson was a vocal supporter of the civil rights movement).