The advent of space-based missions like Kepler has revolutionized the study of solar-type stars, particularly through the measurement and modeling of their resonant modes of oscillation. Here we analyze a sample of 66 Kepler main-sequence stars showing solar-like oscillations as part of the Kepler seismic LEGACY project. We use Kepler short-cadence data, of which each star has at least 12 months, to create frequency-power spectra optimized for asteroseismology. For each star, we identify its modes of oscillation and extract parameters such as frequency, amplitude, and line width using a Bayesian Markov chain Monte Carlo "peak-bagging" approach. We report the extracted mode parameters for all 66 stars, as well as derived quantities such as frequency difference ratios, the large and small separations {Delta}{nu} and {delta}{nu}_02_; the behavior of line widths with frequency and line widths at {nu}_max_ with T_eff_, for which we derive parametrizations; and behavior of mode visibilities. These average properties can be applied in future peak-bagging exercises to better constrain the parameters of the stellar oscillation spectra. The frequencies and frequency ratios can tightly constrain the fundamental parameters of these solar-type stars, and mode line widths and amplitudes can test models of mode damping and excitation.