We present a variational calculation of the spin wave excitation spectrum of double-exchange ferromagnets in different dimensions. Our theory recovers the random phase approximation and 1S expansion results as limiting cases and can be used to study the intermediate exchange coupling and electron concentration regime relevant to the manganites. In particular, we treat exactly the long range three-body correlations between a Fermi sea electron-hole pair and a magnon excitation and show that they strongly affect the spin dynamics. The manifestations of these correlations are many-fold. We demonstrate that they significantly decrease the stability of the ferromagnetic phase and the magnon stiffness. We also show that the ferromagnetic state is unstable against spin wave excitations close to the Brillouin zone boundary. As a result, we find a strong softening of the spin wave dispersion as compared to the Heisenberg ferromagnet with the same stiffness within a range of intermediate concentrations. We discuss the possible relevance of our results to experiments in colossal magnetoresistance ferromagnets. © 2006 The American Physical Society.