Since many inorganic compounds contain some type of metal (alkali, alkaline, transition, etc.), they tend to be able to conduct electricity. For example, while in the solid state, inorganic compounds are poor conductors of electricity. However, in the liquid phase, inorganic compounds are highly conductive. In this phase, inorganic compounds' electrons are able to move very freely, and this movement of electrons is noted as electricity.
Due to ionic bonding typically found in inorganic compounds, they are held together very rigidly and possess extremely high melting and boiling points. Another distinct characteristic of inorganic compounds is their color. Transition metal inorganic compounds, even sitting on a bench-top, are usually highly colored, and this is, again, due to the configuration of the 'd-block' electrons.
The bright and beautiful colors that one sees when fireworks explode is due to the inorganic metal (usually an alkali or alkaline one) present in the compound. Because inorganic compounds display a unique color when burned, this can be used as a 'marker' to identify the metal involved.
Also, inorganic compounds are typically highly soluble in water. That is to say, they can 'disappear' when placed into water since they will simply dissolve. Yet another revealing characteristic of inorganic compounds is their ability to form crystals. The nature of the bonding found in inorganic compounds lend them to be able to grow crystals in saturated solutions.