We consider Friedmann cosmologies with minimally coupled scalar field. Exact solutions are found, many of them elementary, for which the scalar field energy density, rho_f, and pressure, p_f, obey the equation of state (EOS) p_f=w_f\rho_f. For any constant |w_f|<1 there exists a two-parameter family of potentials allowing for such solutions; the range includes, in particular, the quintessence (-1<w_f<0) and `dust' (w_f=0). The potentials are monotonic and behave either as a power or as an exponent for large values of the field. For a class of potentials satisfying certain inequalities involving their first and second logarithmic derivatives, the EOS holds in which w_f=w_f(\f) varies with the field slowly, as compared to the potential.