"Well, until you have two or three callbacks that respond differently to fs.readFile and you start running out of function names, right?"
That's a red flag right there. If you can't figure out a unique name for the callback, perhaps it's not worth naming it.
If you have a reusable piece of code, or it's just getting unwieldy (~3 levels deep or so), then you should consider breaking it out into it's own function. But otherwise for simple things I think it's more readable to have it inline.
It's unfortunate JavaScript's anonymous function syntax is so verbose. It would be much more pleasant with lightweight syntax (CoffeeScript, perhaps?)