That depends on the desired outcome, and the kind of (ab)use it will see. Are you looking for something that will keep brush, water, etc out? Or are you looking for something that will keep big rocks out? If you are looking for a "splash shield", aluminum will be fine. If you have access to a dimple die and press, you can get away with relatively thin material. On the other hand, if you are wanting something more substancial, steel is the way to go. The only problem is finding a source that will sell less than full size pieces. So call around and see if they sell remanents. For a typical non-supporting skid plate, 1/8" (.120) will be fine. If it is going to be a supporting structure (something you will use a jack on, support drivetrain components, etc.), I recommend nothing less than 1/4" for large flat plates. Obviously, things built out of round or square tube can be much thinner as the shape of the material adds significant strength to the product. Likewise, flat plates can be strengthened by adding gussets in appropriate places.
How big of a plate are you considering (length, width...)