MIMF

There are probably a lot of opinions on this topic, but I'm still going to ask.
As the title says:
Is there a most desirable height for strings above the body?
I remember reading somewhere that anywhere from 3/8 at the lower end, to 3/4 at the higher.

Opinions??

3/4 of an inch would be very hard as there would be the tendency to be sharp the further down the fret board you go.
Having very low action can have issues with string buzz too.

1/2" string height at the bridge would seem to be about the norm and always gives me good results with just the right amount of bridge torque.

ahh above the body. I misread and thought above the neck. nevermind my last statement.

One of the reasons I ask is the difference between a Fender style bridge, which is low, and a T.O.M. style which is higher.
The other reason is picking comfortability.
Yet another, is how thick to make a fret board on a neck through. That thickness is really the only way to control the height above body measurement, on a zero angle neck.

You have to consider neck angle when looking at the differences between a fender style bridge and a TOM bridge. A higher bridge will require a larger neck angle. I've never made a fender style instrument, it is possible that they have no neck angle at all. Draw your plan out full scale from the side view. This will help you determine how to handle the variables (neck angle, bridge height, fretboard thickness. . .).

Bryan: One can achieve much the same results with a zero neck angle but the fretboard raised above the level of the body.

It's really a player preference on an electric. Fender-style could be as close as 3/8"(recessed pickups), while a Rickenbacker-style(surface mounted pickups) would be closer to 1".
If they get over 1/2", it's often helpful to have a raised pickguard, like a Les Paul.
On an acoustic, it's important because it determines the rotational force on the bridge, and 1/2" is the typical target.

Exactly. You can manipulate the variables to get to where you want as long as you understand how they relate. This is why drawing it out is so helpful.

Gordon, the "optimum string height above the body" varies with a dozen different parameters - most noticeably with the "setup" (action at nut and upper fretboard, relief) but also by the neck angle, whether the neck stands proud of the body and by how much, type of bridge and its adjustment range, fretboard radius and height of frets. My goal is that if the action is suitable for the player AND there is sufficient adjustment at the bridge/saddles THEN the height above the body must be correct.

A better design parameter where the fretboard plane (actually the frets) strikes the bridge. For a "normal" acoustic a straightedge on the frets should more or less touch the top of a bridge (normally 3/8), with 1/8 of saddle and a playable action that would put the strings about 1/2 inch or so off the top.

Many people who build Fender style bolt on necks and flat tops make the neck pocket 5/8 (0.625) deep. The necks are normally 3/4 plus 1/4 of fretboard, but Fenders usually have 9 to 12 inch radius. I just measured a Fender style neck with jumbo frets - it is 1.072 in the center and 1.020 at the edges. That would mean that the fret line is somewhere between 0.040 and 0.045 above the body - add whatever action you like to that and carry it to the bridge. Remember that the saddles will be adjusted to the fretboard radius - I have seen many with the E strings at the bottom of their travel. Of course you can always shim a Fender neck to fine tune this.

I build set neck carved topped guitars (Les Paul clones) with 3-1/2 degree neck angles and that seems to work out to about 0.625 at the bridge, which seems to work fine with the ToM bridges that I buy (be sure to measure mounting studs and whatever hardware). In fact I made a little dummy ToM that I tape on the guitar while I'm setting the neck - its height is the lowest adjustment of the ToM and if the fret line is just below that I seem to be OK. This is a bit more critical 'cause once you glue the neck in you're committed. Obviously through neck would be the same.

Pickups obviously need to be within their working range - with humbuckers you can get different rings and you have adjustment of both the pup and the poles. Single coils often hang from the bridge or pickguards, sometimes screw to the bottom of the cavity. Always good to get all of your hardware before you start, measure and do a side view drawing of your neck and body to make sure.

The build I am in the middle of is a zero angle neck-thru.
I am going with a 9/32" fret board, with a 12 inch radius. The frets are .100 high. With a good low action the bridge height should be approx. 1/2 inch.
The back of the neck will be about 1/2 at the nut, and 9/16 at the 15th fret.
This will give me a neck thickness of 25/32 at the nut. Should be comfortable at just over 3/4 inch.