I consider the time evolution of observables in the transverse field Ising chain (TFIC) after a sudden quench of the magnetic field.  I present exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter.  These results are based on two complementary approaches based on asymptotic evaluations of determinants and form-factor sums.  I show that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE).  The approach to the stationary state can also be understood in terms of a GGE. Generalizations to particular quenches in other integrable models are discussed.