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What does the distance between a pickup and strings do for the sound? Should active and passive pickups be treated differently?

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The distance from the pickup to the strings determines - in simple terms - the strength of the magnetic field acting on the strings. Since a standard magnetic pickup (active or passive) is an electromagnetic transducer, the output voltage is generated when a string vibrates in a magnetic field.

So far so good, what of the pickup height? The stronger the magnetic field around the string - achieved by bringing the magnetic polepieces closer - the higher the output generated. However, in this world you never get something for nothing: a stronger magnetic field will dampen the vibration of the strings, decreasing sustain.

Thus, finding the right pickup height is a matter of compromise and experimentation. You'll probably want the pickups high enough to generate a healthy signal, but low enough to allow the strings to vibrate freely. The exact height will depend on the strength of the magnets in the pickup.

Active pickups simply incorporate additional preamplification circuitry, so the principle is the same as for passive pickups.

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+1 good answer. You covered pretty much everything, so nothing more to say 'bout this topic. Well, maybe that typically a humbucker has a higher effect on the strings than a single-coil. (obviously) And that the amount of pick-ups is also important, which is one of the reasons why guitars with just one pick-up in the bridge-position are getting more popular "these days". The question is, what has more impact on the strings, pole-piece magnets or blade-magnets? I've always been wondering about that... – Anonymous May 16 '11 at 7:11
The last question would probably involve examining the magnetic field generated by each - possibly interesting from a Physics standpoint, but I'm not sure whether very practical for us guitarists, especially since height adjustments will generally be determined through experiment. As to the popularity of single-pickup guitars, I've always thought it was more a question of simplicity (especially if the controls consist of a single volume pot), than technical considerations. – Faza May 16 '11 at 7:25
Well, my last question isn't a live-depending-on question, but I think that it's a rather interesting question. And about single-pick-up setups: of course simplicity is important but it has an effect on the sustain, too. My work-in-progress guitar (an old LP-style guitar) currently is stripped down to the minimum: bridge-HB > volume-poti > output-jack. And it has a noticable amount of sustain more compared to the 2 humbucker setup. (It's lighter, too obviously) – Anonymous May 16 '11 at 8:56
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a good place to start as to string distance from string to pick-up pole are...

While fretting a note on your gits highest fret on the High E string the distance from the string to pick-up pole should be the thickness of a "DIME" for a Neck Pick-up

and the thickness of a "Nickel" for a Bridge Pick-up

REPEAT: on your Low E string

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This doesn't answer the question, and is in fact not correct. All players have different preferences for string height. – Dr Mayhem♦ Feb 15 at 9:34
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As mentioned, having the pup close to the strings gives a hot signal and increases the magnetic dampening, but there is also an effect on tone as well. IIRC, having the pickup near the strings is more trebley and having them lower is more middy. (But it may be the other way around). Additionally, with most humbuckers having at least 1 coil with adjustable pole pieces, you can set the pup low and jack up the poles to get a bit of a blend, or set it high with the poles screwed down as far as poss. These sort of settings are far more subtle than the type of pup and moving between bridge and neck positions, so you'll need to experiment to find out what works for you, if you can even tell what's going on.

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