We present cosmological parameters derived from the angular power spectrum of the cosmic microwave background (CMB) radiation observed at 148 GHz and 218 GHz over 296 deg^2 with the Atacama Cosmology Telescope (ACT) during its 2008 season. ACT measures fluctuations at scales 500<l<10000. We fit a model for the lensed CMB, Sunyaev-Zeldovich (SZ), and foreground contribution to the 148 GHz and 218 GHz power spectra, including thermal and kinetic SZ, Poisson power from radio and infrared point sources, and clustered power from infrared point sources. The power from thermal and kinetic SZ at 148 GHz is estimated to be B_3000 = 6.8+-2.9 uK^2, where B_l=l(l+1)C_l/2pi. We estimate primary cosmological parameters from the 148 GHz spectrum, marginalizing over SZ and source power. The LCDM cosmological model is a good fit to the data, and LCDM parameters estimated from ACT+WMAP are consistent with the 7-year WMAP limits, with scale invariant n_s = 1 excluded at 99.7% CL (3sigma). A model with no CMB lensing is disfavored at 2.8sigma. By measuring the third to seventh acoustic peaks, and probing the Silk damping regime, the ACT data improve limits on cosmological parameters that affect the small-scale CMB power. The ACT data combined with WMAP give a 6sigma detection of primordial helium, with Y_P = 0.313+-0.044, and a 4sigma detection of relativistic species, assumed to be neutrinos, with Neff = 5.3+-1.3 (4.6+-0.8 with BAO+H0 data). From the CMB alone the running of the spectral index is constrained to be dn/dlnk = -0.034 +- 0.018, the limit on the tensor-to-scalar ratio is r<0.25 (95% CL), and the possible contribution of Nambu cosmic strings to the power spectrum is constrained to string tension Gmu<1.6 times 10^-7 (95% CL).
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