The phenomenon of plasma self-organization in a free-localized high-pressure microwave discharge has been investigated on the basis of the mechanism of ionization-field (IF) instability. Linear and weakly nonlinear stages of discharge evolution have been studied. It has been shown that IF instability at the nonlinear stage, due to the interaction of the harmonics with different wavevectors, can lead to the formation of a rich spectrum of plasma structures, from simple plane plasma autowaves to various 3D spatial structures (helical filaments and three-dimensional Bernard cells).