We derive the galaxy luminosity function in the K_s band for galaxies in 24 clusters to provide a local reference for higher redshift studies and to analyse how and if the luminosity function varies according to environment and cluster properties. We use new, deep K-band imaging and match the photometry to available redshift information and to optical photometry from the SDSS or the UKST/POSS: More than 80 per cent of the galaxies to K ∼ 14.5 have measured redshifts. We derive composite luminosity functions, for the entire sample and for cluster subsamples. We consider the luminosity functions for red-sequence and blue cloud galaxies. The full composite luminosity function has K* = 12.79 ± 0.14 (M_K = -24.81) and α = -1.41 ± 0.10. We find that K* is largely unaffected by the environment, but that the slope α increases towards lower mass clusters and clusters with Bautz-Morgan type < II. The red-sequence luminosity function seems to be approximately universal (within errors) in all environments: It has parameters K* = 13.16 ± 0.15 (M_K = -24.44) and α = -1.00 ± 0.12 (for all galaxies). Blue galaxies do not show a good fit to a Schechter function, but the best values for its parameters are K* = 13.51 ± 0.41 (M_K = -24.09) and α = -1.60 ± 0.29: We do not have enough statistics to consider environmental variations for these galaxies. We find some evidence that K* in clusters is brighter than in the field and α is steeper, but note that this comparison is based (for the field) on 2MASS photometry, while our data are considerably deeper.