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 and the behavior of line widths with frequency and line widths at with , 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.