Wood shingles (photo 1) are combustible, but can be treated at the mill with fire-retardant chemicals. However, the fire-retardant properties of these chemicals become less effective with weathering, http://primeex.comxa.com and can be overcome if the shingles are painted or stained.
Asphalt shingles or roll roofing are made of asphalt with natural fiber or glass fiber felt and are combustible. These are surfaced with mineral grit (like sand) to give them color and to make the surface less ignitable.
Tile roofs (photo 2) are made of overlapping and interlocking terra cotta or concrete tiles, which are not combustible. Tile roofs provide precarious footing when intact, and become slippery when wet, and impossible when covered with broken pieces of tile that were removed for ventilation.
Slate roofs (photo 3) are made of overlapping slates: http://constructionn.comuv.com natural stone that has been split into thin layers to make roofing materials http://samosvaly.site90.net . These roofs provide precarious footing when intact and become slippery when wet or covered with moss; they become impossible when covered with broken pieces of slate that were removed for ventilation.