We have analyzed far-IR (IRAS) data for a sample of optically selected Seyfert galaxies. The far-infrared emission is uncorrelated, or at best weakly correlated, with the UV-optical emission from these sources. We find the far-IR emission to be extended in a number of objects. We discuss the possibility that Seyfert galaxies are undergoing circumnuclear bursts of star formation. For comparison with the large aperture IRAS data we have also obtained new ground-based measurements at 10 and 20 μm for a sample of 17 Seyfert galaxies. Conclusive evidence for extended 10 and 20 μm emission is seen in 7 out of 17 objects. In addition, almost all of the objects have ground-based fluxes which are smaller than those measured by IRAS. Finally, for five objects the emission appears to be more extended at 10 μm than at 20 μm. This would be expected if the 10 μm emission arose, in part, from a population of very small grains for which single photon heating is important.