We have developed, from scratch, a 3D radiative transfer code based on the Monte Carlo method, that fully takes into account the spherical shape of a planetary atmosphere, multiple scattering, and the polarized nature of light. Accounting for the sphericity of an atmosphere is important for the analysis of observations near the planetary limb and the twilight zone, i.e. the regions on a planet where the parent star and/or the observer are low or even below the local horizon. In such regions, the widely used radiative transfer models that are based on the locally plane-parallel atmosphere approximation can lead to significant errors, especially for planets that have extended atmospheres. With our code, we simulate total flux and polarization signals of light that is reflected by spatially resolved and spatially unresolved planets with extended atmospheres. We discuss the effects due to the atmosphere’s sphericity and compare against computations with a locally plane-parallel code. Our results are relevant both for the interpretation of observations of various Solar System planets and moons (with atmospheres) and for the investigation of total flux and polarization signals of exoplanets at all phase angles, including during transits. Especially hot Jupiters are likely to have extended atmospheres and to be detected in edge-on orbits with transits. During a transit, an extended atmosphere can strongly increase the amount of starlight that is measured, thus leading to a smaller derived planet size. We also specifically simulate the polarimetric signal of Titan, Saturn’s largest moon that is known to have an extended atmosphere. We find that at small phase angles, as observed from Earth, Titan’s limb is strongly affected by the sphericity of its atmosphere and that at large phase angles, as observed by a spacecraft like Cassini, Titan’s brightness increases strongly due to forward scattered light.