I've always wondered, how low of a tire pressure can you safely run, without blowing the bead? I was wondering if it mattered at all, and what the possibility of one blowing at low psi's? Mainly I am wondering, for if I am on soft ground and stuck, how low I can safely lower it to without having to worry about it.

It depends on the situation. I've run 12lbs. on the street from a trail to the gas station and back. I've lost a bead at 22lbs. on a pretty nasty trail.

I probably wouldn't go lower than 10lbs.

What size tire are you running? If your running a 11.5 or 12.5" wide tire on a 15x8 or 15x7, you can safely air down to 15-20 psi without worrying. The only time I lost a bead on my 33s on my old 97 was when I was being a total ass at 101 in Paragon in the mud.