This paper considers feedback stabilization for the infinite-dimensional bilinear system dz(t)/dt = Az(t) + v(t) Bz(t), where A is the infinitesimal generator of a linear C(0)-semigroup of contractions on a Hilbert space H and B : H -> H is a linear bounded operator. Sufficient conditions for exponential and weak stabilization are given. A minimization problem is also considered. Applications to parabolic and hyperbolic equations are presented.