Brass is a commonly used case material. It is resistant to corrosion, the case head can be drawn and work hardened to make useful cases for modern metallic cartridges working at relatively high pressure, and the neck and body portion are easily annealed to make the case ductile enough to allow reforming so that it can be reloaded many times.
Some "plinking" ammunition, as well as some military ammunition (mainly from the former Soviet Union and China) is made with steel cases because steel is less expensive than brass. It is not feasible to reuse steel cases and these rapidly deteriorate in the environment, through rusting. As military forces typically consider small arms cartridge cases to be a disposable, one-time-use, devices these limitations are inconsequential for those applications. However, case weight (mass) affects how much ammunition a soldier can carry, so the lighter steel cases do have a military advantage; conversely, steel is more susceptible to contamination and damage so all such cases are varnished or otherwise sealed against the elements but that seal is relatively fragile and such ammunition must be handled more carefully from the time of manufacture until use.
One downside caused by the increased strength of steel in the neck of these cases (compared to the annealed neck of a brass case) is that propellant gas can blow back past the neck and into the chamber. Constituents of these gases condense on the (relatively cold) chamber wall. This solid propellant residue can make extraction of fired cases difficult. This is less of a problem for guns of the former Warsaw Pact nations, which were designed with much larger chamber tolerances than NATO guns are.