the float in the carb or bad needle and seat or fuel solenoid or could just be dirt in the carb not letting the needle seat and sit off the fuel or the float needs adjusted
Scott is correct. A fix if you don't have time to deal with a carb is to put an in line fuel shut off (about $7 at the big box stores) Then when your done mowing turn off the fuel line til the motor dies. No fuel can gravity feed thru the carb.
If the engine has a crankcase pulse operated fuel pump... it's possible that the diaphragm has ruptured and is allowing fuel to run directly into the crankcase.