Although the dispersion of magnons has been measured in many bulk materials, few studies deal with the changes in the dispersion when the material is in the form of a thin film, a system that is of interest for applications. Here we review inelastic tunneling spectroscopy studies of magnon dispersion in Mn/Cu₃Au(1 0 0) and present new studies on Co and Ni thin films on Cu(1 0 0). The dispersion in Mn and Co films closely follows the dispersion of bulk samples with negligible dependence on thickness. The lifetime of magnons depends slightly on film thickness, and decreases considerably as the magnon energy increases. In Ni/Cu(1 0 0) films the thickness dependence of dispersion is much more pronounced. The measurements indicate a considerable mode softening for thinner films. Magnon lifetimes decrease dramatically near the edge of the Brillouin zone due to a close proximity of the Stoner continuum. The experimental study is supported by first-principles calculations.