The self-organization of a tokamak plasma is a fundamental turbulent plasma phenomenon, which leads to the formation of a self-consistent pressure profile. This phenomenon has been investigated in several tokamaks with different methods of heating. It is shown that the normalized pressure profile has a universal shape for a wide class of tokamaks and regimes, if the normalized radius ρ = r/(IpR/κB)1/2 is used. The consequences of this phenomenon for low aspect ratio tokamaks, the optimal deposition of additional heating, fast velocity of heat/cold pulse propagation and the possibility of obtaining a peaked density profile in ITER are discussed.