Crop classification is an important remote sensing task with many applications, e.g., food security monitoring, ecosystem service mapping, climate change impact assessment, etc. This work focuses on mapping 10 crop types at the field level in an agricultural region located in the Spanish province of Navarre. For this, multi-temporal Synthetic Aperture Radar Polarimetric (PolSAR) Sentinel-1 imagery and multi-spectral Sentinel-2 data were jointly used. We applied the Cloude–Pottier polarimetric decomposition on PolSAR data to compute 23 polarimetric indicators and extracted vegetation indices from Sentinel-2 time-series to generate a big feature space of 818 features. In order to assess the relevance of the different features for the crop mapping task, we run a number of scenarios using a Support Vector Machines (SVM) classifier. The model that was trained using only the polarimetric data demonstrates a very promising performance, achieving an overall accuracy over 82%. A genetic algorithm was also implemented as a feature selection method for deriving an optimal feature subset. To showcase the positive effect of using polarimetric data over areas suffering from cloud coverage, we contaminated the original Sentinel-2 time-series with simulated cloud masks. By incorporating the genetic algorithm, we derived a high informative feature subset of 120 optical and polarimetric features, as the corresponding classification model increased the overall accuracy by 5% compared to the model trained only with Sentinel-2 features. The feature importance analysis indicated that apart from the Sentinel-2 spectral bands and vegetation indices, several polarimetric parameters, such as Shannon entropy, second eigenvalue and normalised Shannon entropy are of high value in identifying crops. In summary, the findings of our study highlight the significant contribution of Sentinel-1 PolSAR data in crop classification in areas with frequent cloud coverage and the effectiveness of the genetic algorithm in discovering the most informative features.