I've never seen a job that doesn't have salary advertised alongside it (okay, well I've seen some say "competitive salary" but that's just code for "uncompetitive salary") though so you should know what they're offering anyway. Typically I ask for a bit above what they're offering to try it on, but often it is a genuine hard cap.
Of course it could depend where you are, if you're in the US the approach to this sort of thing may well be different to here in the UK.
I've tried going for jobs that offer less in the hope I can convince them to offer me more after recruiters have convinced them but it never works, their advertised hard cap is their hard cap and no amount of persuasion will convince them (one company made me do some up to 3 hour technical test, and I scored 99.6% on it, the highest they've ever seen by far and they still offered me their cap which was Â£5k lower than the minimum I made it clear I was willing to accept).
But ultimately if a job isn't advertising a headline salary that I'd be happy with then I just don't go for it any more, I don't see the point, it wastes my time and theirs, that's why I tell recruiters exactly what I'd move for as a minimum, what I'd like and so forth and the recruiters typically respect that - it's in their interest to get you your high end figure because then they get more too. If I expected more I'd have gone for a higher headline figure job in the first place.
As I say though it may well be down to societal differences between the US and UK.