Safe pressure to let tyres down to

gday zapper.
with out bead locks i wouldnt go under 10-12 psi if your planing on leaving them low for a lond drive but for short distance 6-8psiRaphus cucullatus

With or without tubes.

With Tubes, 8-10 is kewl,
without probably 10-15, Im going to try that on the weekend, around 10psi

I have tyres like that on my landcruiser which weighs 1850 kg and I wouldnt go under 15 psi normally.But if I was bogged on a tidal flat in an area with 5metre tides I would let them down to 5 psi or more if I had to.How far you let them down depends on the strength of the tyre wall .A light 4x4 with stiff sidewalls may require 10 psi minimum.It something you decide on based on experience and there are no hard and fast rules.
On long offroad trips,having tyres with a low inflation will cause them to over heat in the sand and cause the ply to separate.It may not be apparant till your back on the bituman at high speed.

Zapper,
A good answer from Ross, as he mentioned I put this down to experience with your own vehicle, initially follow some guide lines as mentioned above by others but as I've found out it very much comes down to the tyres and the weight of your vehicle. My opinion.Keep the shiny side up

buy seconds airs and then you can go as low as you want and never have a tyre come off the bead :D

100% street legal too

As others have mentioned, you can go very low, if you drive slowly and don't turn sharply. Main think is not to turn sharply or fast, otherwise you'll roll a tyre off a front rim. If you do roll off a tyre, we usually find that after cleaning out the sand, most tyres can be reinflated with a good pump, especially if only the outer bead has come off.

Zapper
the answers above are a good guide,the lowest i have gone is to the point of not registering on the gauge But travelled only a few 100 m the reinflated,the safe answer is as low as you have to go to maintain or gain momentom then reinflate, but between 10 - 20 psi is usualy safe. also remember the lower the preasure the lowwer the speed
regards Bruce