Lighting/textures – if you shake your head, subtle specular highlights can become apparent on surfaces that otherwise look completely matte.
Fresnel effect/Fresnel reflection/Facing ratio/Surface ratio
Fresnel reflection is the phenomenon where the surface's reflectivity is a function of the viewing angle of the surface. The material is more reflective at a grazing angle than it is when looking straight at it (normal to the surface).
Fresnel effect/Surface ratio can be seen in a pond. If you look across the pond (more tangent to the surface), the surface of the water looks very reflective and you can barely see through it, but if you look straight down into the water (along its normal), the water appears almost completely transparent.
Often, you might want to use a texture that doesn't tile and is too small to spread across the entire object without tiling. The repeating pattern of the texture will be noticeable if it is used as the diffuse channel of the material, which is unacceptable. However, you might still be able to get some use out of that non-tiling texture by using it in other channels instead of the diffuse. Use a flat color for the diffuse, and then you can try using the texture as a reflection map, spec map, bump map, or anisotropy map. The repeating pattern won't be noticeable in those channels, but the texture can still add some very significant qualities to the surface to break it up. Actually, I'm not sure that this is true - the repeating pattern still might be visible in other channels besides the diffuse?
All materials have some amount of fresnel reflection except for metals, which appear reflective from any angle.
Metals do not have a fresnel reflection - they appear reflective from any angle.