I'm surprised at how many here have not seen minimum pressures labeled. I see it often, and I take to to mean pressure below which you may get a pinch flat, or bead rolling off the rim, or the tire shifting during braking. I see a lot of bikes with valve stem damage due to low tire pressure.

One of the best arguments I've heard for tubeless tires came from a MTBer who said tubeless allows him to use extremely low pressures in some terrain, without worrying about a pinch flat.