We report spin wave propagation experiments in thin yttrium iron garnet (YIG) films. Using time-resolved scanning Kerr microscopy we extract the mode structure of the spin waves. For quasi-single-mode excitation, the spin wave decay can be fitted with a damped harmonic oscillator function providing us with information about the attenuation length. We measure values of about 2.7 and 3.6 mu m for the spin wave decay length of 38- and 49-nm-thick YIG samples, respectively. Micromagnetic simulations are performed to compare experimental and simulated modes. The data are in very good agreement with these simulations.