bernie I'm hardly an expert (tdpri will have some super in depth posts on it)

Historically...

They're staggered to compensate for the radius of the fretboard (strat's are between 7.5 - 12in usually).

AND

They're staggered to compensate for the output of the individual strings (think physics = the thicker a string the more it'll vibrate/resonate).

Doesn't really explain blade or rail style pickups, but then they're usually used on humbucker designs on guitars with a flatter fretboard (16in & up).

Are they adjustable...? Welllllllllll, kinda. Not really. Maybe. It depends. And I wouldn't - unless the pickup was specifically designed to be easily adjusted.

But pickup height IS easily adjusted and - once we put aside the debate over tonewoods and all that - is becoming regarded as one of the biggest influences over tone (and obviously volume). So that is something to play around with - just mark where they are currently before you start tweaking! And bear in mind that they are magnets, so to0 low is a bad thing as they'll pull on the strings (aka “Stratitis”) damping that vibration that actually makes the sound.

Too high means little volume and your lovely toob amp won 't howl at the neighbours like you want it too.

Thanx V8. Makes lots of sense.

bernie
How brave are you?
The magnet stagger might not suit your current strings and fretboard radius, and does influence sound. You could try it, it has been done (I have), you could take out the pickup, support it well, and push the pole to where you want it. Google Kinman Stagger, Vintage Stagger, Modern Stagger to get all the ideas on stagger.
You can destroy the pickup by pushing the poles around, by shorting or breaking the coil wires.
As for pickup height, many ideas and opinions too. Generally, you do not want the magnets too close to the string, it does damp vibrations.
Adjusting the pickups to sit further from the strings seem to give a mellower, smoother tone. You may loose a bit of volume, but the sound might be what you like. Also, adjust the heights to try and balance volume between the pickups. And, adjust bass and treble sides to try and get an even response across the strings.
A way to play with polepiece heights/stagger is to put some shims on the poles (small washers) to vary heights, that way you can hear what the effect of altering the stagger might be.
It is well worth toying with this. I prefer the pickups further away from the strings than normal factory recommendations.

The magnetic field lines between poles should push each other out of the way (like polarity), but I will have to google it to see the ecact pattern.
Having the poles further from the string should have a bigger volume of field lines at the string, "including" more string length in the field lines, picking up more vibrations and harmonics - "wider" sound. But, not sure. Must read up on it again.