Updated constraints on the dark matter cross section and mass are presented combining cosmic microwave background (CMB) power spectrum measurements from Planck, WMAP9, ACT, and SPT as well as several low-redshift data sets (BAO, HST, and supernovae). For the CMB data sets, we combine WMAP9 temperature and polarization data for $l\ensuremath{\le}431$ with Planck temperature data for $432\ensuremath{\le}l\ensuremath{\le}2500$, ACT and SPT data for $l>2500$, and Planck CMB four-point lensing measurements. We allow for redshift-dependent energy deposition from dark matter annihilation by using a ``universal" energy absorption curve. We also include an updated treatment of the excitation, heating, and ionization energy fractions and provide an updated deposition efficiency factors (${f}_{\text{eff}}$) for 41 different dark matter models. Assuming perfect energy deposition (${f}_{\text{eff}}=1$) and a thermal cross section, dark matter masses below 26 GeV are excluded at the $2\ensuremath{\sigma}$ level. Assuming a more generic efficiency of ${f}_{\text{eff}}=0.2$, thermal dark matter masses below 5 GeV are disfavored at the $2\ensuremath{\sigma}$ level. These limits are a factor of $\ensuremath{\sim}2$ improvement over those from WMAP9 data alone. These current constraints probe, but do not exclude, dark matter as an explanation for reported anomalous indirect detection observations from AMS-02/PAMELA and the Fermi gamma-ray inner-Galaxy data. They also probe relevant models that would explain anomalous direct detection events from CDMS, CRESST, CoGeNT, and DAMA, as originating from a generic thermal weakly interacting massive particle. Projected constraints from the full Planck release should improve the current limits by another factor of $\ensuremath{\sim}2$ but will not definitely probe these signals. The proposed CMB Stage IV experiment will more decisively explore the relevant regions and improve upon the Planck constraints by another factor of $\ensuremath{\sim}2$.