For most portable generators and power equipment, running out of fuel will simply cause the engine to stop, much like turning off the ignition switch.
Unlike your car, most portable power equipment is not yet fuel injected, and therefore use a simplified fuel delivery system. This means that there is typically no danger to fuel system components such as electric fuel pumps when they run dry either.
Draining the carburetor or fuel system may also be a part of recommended storage procedures. This reduces the chance of the fuel system “gumming up” and requiring service. An easy way to do this can be to turn off the fuel valve while the equipment is warmed up and running and allow the engine to stop on its own. Check your Owner’s Manual for appropriate methods for your equipment.