It has been suggested that recent cosmological and flavor-oscillation data favor the existence of additional neutrino species beyond the three predicted by the Standard Model of particle physics. We apply Bayesian model selection to determine whether there is indeed any evidence from current cosmological datasets for the standard cosmological model to be extended to include additional neutrino flavors. The datasets employed include cosmic microwave background temperature, polarization and lensing power spectra, and measurements of the baryon acoustic oscillation scale and the Hubble constant. We also consider other extensions to the standard neutrino model, such as massive neutrinos, and possible degeneracies with other cosmological parameters. The Bayesian evidence indicates that current cosmological data do not require any non-standard neutrino properties. ; Comment: 17 pages, 7 figures. v3: replaced with version published in JCAP (typo fixes, including Figure 1 units)