Frank Berto did some analysis, appearing here and here. Surley makes bikes with very fat tires and has some nice discussion about tire pressure here. There is also a thread on the Thorn forum, where I worked out a hypothesis that, using Berto's "uniform drop" theory, should vary proportionally with the load and inverse proportionally with the 3/2 power of the tire width.
I came up with a constant of proportion to give a reasonable fit with the published graphs by Berto. The fit is not very exact though... whether my formula gives better pressures than Berto's graphs can be left as an exercise for the reader/rider. In any case my formula is easily evaluated for a wider range of loads and tire widths than Berto's graphs cover.
Here, then, is a table of suggested tire pressures. Across the top, find the load, in pounds, on the single wheel, e.g. roughly half the total load on the two wheels of a bicycle. Along the left side, find the width of the tire in mm. The number at the corresponding column and row of the table is then the suggested pressure in psi. Click on the table to get the full image which includes higher loads.