  We present the first three-frequency South Pole Telescope (SPT) cosmic
microwave background (CMB) power spectra. The band powers presented here cover
angular scales 2000 < ell < 9400 in frequency bands centered at 95, 150, and
220 GHz. At these frequencies and angular scales, a combination of the primary
CMB anisotropy, thermal and kinetic Sunyaev-Zel'dovich (SZ) effects, radio
galaxies, and cosmic infrared background (CIB) contributes to the signal. We
combine Planck and SPT data at 220 GHz to constrain the amplitude and shape of
the CIB power spectrum and find strong evidence for non-linear clustering. We
explore the SZ results using a variety of cosmological models for the CMB and
CIB anisotropies and find them to be robust with one exception: allowing for
spatial correlations between the thermal SZ effect and CIB significantly
degrades the SZ constraints. Neglecting this potential correlation, we find the
thermal SZ power at 150 GHz and ell = 3000 to be 3.65 +/- 0.69 muK^2, and set
an upper limit on the kinetic SZ power to be less than 2.8 muK^2 at 95%
confidence. When a correlation between the thermal SZ and CIB is allowed, we
constrain a linear combination of thermal and kinetic SZ power: D_{3000}^{tSZ}
+ 0.5 D_{3000}^{kSZ} = 4.60 +/- 0.63 muK^2, consistent with earlier
measurements. We use the measured thermal SZ power and an analytic, thermal SZ
model calibrated with simulations to determine sigma8 = 0.807 +/- 0.016.
Modeling uncertainties involving the astrophysics of the intracluster medium
rather than the statistical uncertainty in the measured band powers are the
dominant source of uncertainty on sigma8 . We also place an upper limit on the
kinetic SZ power produced by patchy reionization; a companion paper uses these
limits to constrain the reionization history of the Universe.
