New Nemo Tensor Insulated came rolled up. Store it rolled up or flat? Either way, valve open, I know.

Instructions from the source, Tom:

Nemo Care

Ha, didn't even think of looking there, thanks. Interesting that they come from the factory compressed if they don't think they should be stored that way.

Well, it would be hard to ship otherwise, and hard to pack on your trip ;), but I think there's probably a difference between occasional short-term compression and long term storage.

There is such a variety of pads (and other equipment) these days made from different materials and technologies that there's no one answer to your question. For example here's the manufacturer's recommendation for mine:

Storage Recommendations Your air mattress can be completely deflated and rolled tight for storage. We recommend leaving the valve open and storing your mattress in a stuff sack to protect it from dirt and sharp objects. For the smallest packed size, completely deflate the mattress, fold in thirds lengthwise and roll toward the valve end to push any extra air out of the mattress.