We use pretty much everything.  Most of our flats are muslin.  We have some luan or paneling, and some plywood.  We have phased out styrophome as a bad idea, since I build most of the flats.

When I arrived at my current theater, a little over a season and a half ago, I was appalled to find a large stack of sheetrock poorly toed and sliding down 'til it was a flat pile on the floor. I thought, "who in their right mind would EVER purchase sheet rock for set construction?" I have since learned that the sheetrock was a donation (and we all know what to do with donations). So, I bit my tongue and have even used it myself to save production costs, but once it comes down it goes to the trash, 'cause once there's a drill hole through it or a corner gets crushed it just crumbles into a semi fine powder . we're slowly getting back on track with Luan.

We have incredibly poorly framed flats, with muslin.  We've also used a bit of plain cardboard, mostly to screen stuff backstage.  We did an interactive murder mystery (single day, on site at various locations) with sets built entirely from cardboard and duct tape.  (Duct tape is too expensive... we should've used plywood or something).

switched a few years ago to luan    works and stores better than Muslin.

    I must say that some of the older muslin flats that have had layers upon layers of paint are now just has hard as the luan  or at least it seems so!