We present constraints on cosmological and astrophysical parameters from high-resolution microwave background maps at 148 GHz and 218 GHz made by the Atacama Cosmology Telescope (ACT) in three seasons of observations from 2008 to 2010. A model of primary cosmological and secondary foreground parameters is fit to the map power spectra and lensing deflection power spectrum, including contributions from both the thermal Sunyaev-Zeldovich (tSZ) effect and the kinematic Sunyaev-Zeldovich (kSZ) effect, Poisson and correlated anisotropy from unresolved infrared sources, radio sources, and the correlation between the tSZ effect and infrared sources. The power ℓ 2 C ℓ /2π of the thermal SZ power spectrum at 148 GHz is measured to be 3.4 ± 1.4 µK 2 at ℓ = 3000, while the corresponding amplitude of the kinematic SZ power spectrum has a 95% confidence level upper limit of 8.6 µK 2. Combining ACT power spectra with the WMAP 7-year temperature and polarization power spectra, we find excellent consistency with the LCDM model. We constrain the number of effective relativistic degrees of freedom in the early universe to be N eff = 2.79 ± 0.56, in agreement with the canonical value of N eff = 3.046 for three massless neutrinos. We constrain the sum of the neutrino masses to be Σm ν < 0.39 eV at 95% confidence when combining ACT and WMAP 7-year data with BAO and Hubble constant measurements. We constrain the amount of primordial helium to be Y p = 0.225 ± 0.034, and measure no variation in the fine structure constant α since recombination, with α/α 0 = 1.004 ± 0.005. We also find no evidence for any running of the scalar spectral index, dn s /d ln k = −0.004 ± 0.012.