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I've recently read about wire meshes and other such things being added onto tanks in order to try to defeat shaped charge explosives by prematurely detonating them. How effective was this, and how widespread was its use?

First, the use of stand-off protection against shaped charges was very effective. The Germans began attaching first wire mesh, and then solid metal, panels on outriggers to detonate HEAT-style rounds before they struck the main armour body of the tank. Chiefly found on the PzKpfw III and IV, and the StuG models, the use of these panels was sometimes compromised by the inferior methods used to attach them; panels would often be torn off by travel through forest or urban terrain, leaving sections of the tank unprotected.

Most of the other nations involved did not produce "official" stand-off panels or systems to protect against shaped-charge rounds. But the crews were innovative in fashioning "supplemental" armour that fulfilled two purposes: it prevented solid AP rounds from penetrating by causing it to expend most of its kinetic energy before reaching the vehicle's base armour, and it gave shaped-charge rounds an extra level of armour to defeat, which the plasma jet usually couldn't.

I don't know how wide spread it was aside from the Germans.

Shaped charges have an optimum stand off distance to allow the jet of gas and liner material to form. It is a focused explosion (think of a lens,bad analogy but best I can do at the moment) too close and the jet may be too wide or have other problems. detonated too far away and the jet becomes unfocused and disapates some of it's energy in open air. The greater the distance from the armour the better the mesh (or metal screen) would work. Against modern shaped charge warheads the distance is measured in feet, some times over 10 feet.!!!
Screens tend to work on hull sides were the screen detonates the charge at least the with of the track away or on turrets that are small enough that the addition of a screen a foot or two out from the turret side doesn't overhang the hull side by much when turret turns.
Trying to add screens that extend beyond the actual shape of the tank (front or rear, or further out from side) would either limit tanks ability to negotiate obsticals or result in the screens getting knocked off before combat. see many photos of German MK IIIs and MK IVs with pannels missing from their screens.

Unfortunatly the actual percent of protection that the screens gave would vary with each different shaped charge used aginst it and even with impact angle so trying to figure out game usage is only an average.

Optimum stand off distance for shaped charge is a multiple of it's diameter and a function of it's specific design. I have seen a chart for this but it related more towards modern weapons than WWII so I would hesitate to use it's information here.

Most of the supplemental armour Flash speaks of was more in the nature of "feel good" armour for the crew. Consider the following.
Penetration figures for .50 call ball ammo. 1930's loading, MV 2500fps.

at 200yds it would penetrate 1/4 in armour, against 3/8 in armour it would penetrate only 0.1 in. But it would penetrate 6in of concrete or about 15in of sand (give or take, depending on wet or dry) or over 11in of gravel.

If you had a cannon that would penetrate 4in or more of armour I doubt that a box of gravel or two layers of sand bags was really going to stop the round. it might cause it to deflect slightly and change the impact angle???
As far as sandbags vrs shaped charges, this could be the start of ceramic armour[:D]