Generally, for most off road vehicles 15-20 PSI is a good starting point compared to 35 PSI +/- found on most stock tires. For very soft sand - such as dune running - 10 PSI may be optimal but at tire pressures that low, you are risking the tire coming off the bead.
You want maximum traction when you venture off road. One of the most effective techniques to increase off-road traction is to air down your vehicle's tires. A simple drop in pressure can be the difference between making it up and over, or simply spinning your wheels.
Airing down will give you more traction off road, whether you're in sand, snow, dirt, rocks, or mud. Recommendations going down to as low as 15 lbs. of air for wheels without bead locks when going off road. When running a lower pressure, he says you'll want to keep an eye on things, just to be on the safe side. After all, popping a bead won't be much fun on the trail.
If your rig does have wheels equipped with bead locks, you can go far lower in pressure, which often allows better traction, especially in the tough stuff you could possibly runs as low as 3 lbs. of air when going off road with vehicles on bead locks.
Another interesting point: If you're towing a trailer across the sand, for example, air down the trailer tires to about 15 lbs., too. This aids in flotation, and will help guard against the trailer's tires sinking into the sand. You're probably not going to want to tow the trailer up big hills, but it should help across the flats.
The most important thing about airing down is actually airing back up. You do not want to drive on the paved roads with tires that have been aired down below the recommended pressure. Driving at speed on aired-down tires can cause damage to the tire, and possibly cause a blow out. So, be sure to air those tires back up before returning to the pavement. There are numerous portable air compressors and air accessories that you can take with you, so you can air up before hitting the highway.
This is where the Mega-Mikes Hydro3 comes into play by providing a convenient, recessed, readily available air compressor outlet.
Many people have different opinions as to how much to air down when off roading, so find what works for you and your setup. But be sure to be careful, and air up before venturing back onto the pavement.