Slate is a relatively soft, flakey stone. Being highly porous and absorbant, it can become popular to use for drink coasters. It takes engraving very well.
While we cannot mark on bare metal, when the surface has been annodized, painted or otherwise coated we can engrave away the coating to reveal the bare metal underneath.
Most types of glass engrave beautifully. Glass is unique in that it does not get cut into, but rather foams up for a subtle raised engraving. Some glass can also be vector - scored for hand-cutting.
Glass mirror engraves just like regular glass, and it can also be cut from behind to reveal a subtle image inside the shiny mirrored background.
Ceramic tile, whether bare or glazed, can be engraved with great results. Bare tile sometimes can't hold highly detailed images, but glazed tile is similar to glass and engraves very well.
Popular for interior design, most marble will engrave well. It is very helpful with this material to have an extra piece from the same project that can be tested prior to running large amounts.
Many types of stone can be engraved, but they may react very differently depending on hardness. The harder the stone is the more it will just fracture the surface instead of fully engraving.
Clay / Terra Cotta
Both clay tiles and handmade clay objects will engrave well in the laser. Different types of clay and finishes may alter the exact look of the final result.