We predict that spin-waves in an easy-plane ferromagnet have a finite lifetime at zero temperature due to spontaneous decays. In zero field the damping is determined by three-magnon decay processes, whereas decays in the two-particle channel dominate in a transverse magnetic field. Explicit calculations of the magnon damping are performed in the framework of the spin-wave theory for the XXZ square-lattice ferromagnet with an anisotropy parameter λ<1. In zero magnetic field the decays occur for

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... ^*<λ<1 with λ^*≈ 1/7. We also discuss possibility of experimental observation of the predicted effect in a number of ferromagnetic insulators.