Self-diffusion coefficients D for water, benzene, and cyclohexane were determined in high-temperature conditions along the liquid branch of the coexistence curve and in supercritical conditions including an extremely low density region. The diffusion data available in literature were compared and evaluated. A fifth-order polynomial for In D with the single variable T(-1) On(D/10(-9) m(2).s(-1)) = a(0)+ a(1)x + a(2)x(2) + a(3)x(3) + a(4)x(4) + a(5)x(5) with x = 1000/(T/K)) was found to provide good fitting along the liquid branch of the coexistence curve. A single polynomial function for the scaled quantity rho D/T(1/2) with the two variables, density p and temperature T(-1) (third-order polynomial of p and and the cross terms), can universally represent the diffusion data over a wider range including both the gas liquid coexistence and the extremely low density conditions. The function gives a reliable and reasonable behavior of D in the medium-density supercritical states in which the experimental uncertainty is rather large clue to the severe conditions. The temperature and density differentials thus obtained were used to shed light on the effect of hydrogen bonding that makes water different from nonpolar organic liquids. The temperature dependence of the self-diffusion coefficient for water is larger than those for organic liquids, due to the large contribution of the attractive hydrogen-bonding interaction. The density dependence is larger for organic liquids than that for water.