It will print onto anything is what most sales idiots used to try to profess and to a degree it is true... but does the ink adhere well is the question you need to be asking. My flatbed can print up to 4" thick material, but I have never had anyone ask for it. Normally you will print no more than 1" thick material and usually 3/16" or 1/4" is everyday thickness.
Be aware that the material needs to be good and flat as having a major headstrike with UV printheads would be a bit costly, so ensure your vacuum system can suck down any curvatures in your media.
I have also gone the other way and printed 4 mil polyethylene bags for product mockups with white underneath and heat sealed them to look like final product (actually looked way better than the full flexo print run in the end).
So anyway... to answer your question... here is a brief list...
Extruded PVC (Sintra/Komatex/Palight/Excel/Foamacell/etc.)
Styrene
Foamcore
Gatorboard
Dibond (Alumapanel/Alumacore/MaxMetal/etc.)
Aluminum sheets
PETG
Acrylic
Polycarbonate
Cardboard
Posterboard
Carpet
Corrugated plastic
Ultraboard
Wood based products
Tables
Doors
Ceiling Tiles
Light diffusers
Ceramic tiles
Styrofoam
you get the point...