Insulators have zero density of states at the Fermi level due to their band gaps. Thus, the density of states-based electronic entropy is essentially zero in these systems.
Metals have non-zero density of states at the Fermi level. Metals with free-electron-like band structures (e.g. alkali metals, alkaline earth metals, Cu, and Al) generally exhibit relatively low density of states at the Fermi level, and therefore exhibit fairly low electronic entropies. Transition metals, wherein the flat d-bands lie close to the Fermi level, generally exhibit much larger electronic entropies than the free-electron like metals.
Oxides have particularly flat band structures and thus can exhibit large , if the Fermi level intersects these bands. As most oxides are insulators, this is generally not the case. However, when oxides are metallic (i.e. the Fermi level lies within an unfilled, flat set of bands), oxides exhibit some of the largest electronic entropies of any material.
Thermoelectric materials are specifically engineered to have large electronic entropies. The thermoelectric effect relies on charge carriers exhibiting large entropies, as the driving force to establish a gradient in electrical potential is driven by the entropy associated with the charge carriers. In the thermoelectric literature, the term band structure engineering refers to the manipulation of material structure and chemistry to achieve a high density of states near the Fermi level. More specifically, thermoelectric materials are intentionally doped to exhibit only partially filled bands at the Fermi level, resulting in high electronic entropies. Instead of engineering band filling, one may also engineer the shape of the band structure itself via introduction of nanostructures or quantum wells to the materials.