We use Bayesian model comparison to determine whether extensions to Standard-Model neutrino physics — primarily additional effective numbers of neutrinos and/or massive neutrinos — are merited by the latest cosmological data. Given the significant advances in cosmic microwave background (CMB) observations represented by the Planck data, we examine whether Planck temperature and CMB lensing data, in combination with lower redshift data, have strengthened (or weakened) the previous findings. We conclude that the state-of-the-art cosmological data do not show evidence for deviations from the standard (ΛCDM) cosmological model (which has three massless neutrino families). This does not mean that the model is necessarily correct — in fact we know it is incomplete as neutrinos are not massless — but it does imply that deviations from the standard model (e.g., non-zero neutrino mass) are too small compared to the current experimental uncertainties to be inferred from cosmological data alone.