Spectropolarimetry is a powerful tool for characterising planetary atmospheres and surfaces. For the design and operation of spectro(polari)metric instrumentation, numerically simulated signals of the measured radiation are essential. Here we present MONKI (Monte Carlo KNMI), an efficient and accurate radiative transfer code written in Fortran, based on the Monte Carlo method. MONKI computes both total and polarised radiances reflected and transmitted by a planetary atmosphere, fully accounting for the polarisation of light in all orders of scattering. MONKI can handle atmospheres that are horizontally homogeneous, as well as those with horizontal inhomogeneities, such as three-dimensional (3D) patchy clouds. We validate MONKI through comparisons with various other radiative transfer codes and demonstrate that it converges reliably even for optically thick and strongly polarising atmospheres. Finally, we present sample simulations of sunlight reflected by the Earth and Venus, and explain the total and polarised radiance features by analysing the altitudes at which the photons are scattered. We conclude that MONKI is a versatile and accurate tool, suitable for simulations and detailed analyses of locally reflected light by the Earth, Venus, and, in principle, any other planet.