Efficient methodologies for mapping croplands are an essential condition for the implementation of sustainable agricultural practices and for monitoring crops periodically. The increasing spatial and temporal resolution of globally available satellite images, such as those provided by Sentinel-2, creates new possibilities for generating accurate datasets on available crop types, in ready-to-use vector data format. Existing solutions dedicated to cropland mapping, based on high resolution remote sensing data, are mainly focused on pixel-based analysis of time series data. This paper evaluates how a time-weighted dynamic time warping (TWDTW) method that uses Sentinel-2 time series performs when applied to pixel-based and object-based classifications of various crop types in three different study areas (in Romania, Italy and the USA). The classification outputs were compared to those produced by Random Forest (RF) for both pixel- and object-based image analysis units. The sensitivity of these two methods to the training samples was also evaluated. Object-based TWDTW outperformed pixel-based TWDTW in all three study areas, with overall accuracies ranging between 78.05% and 96.19%; it also proved to be more efficient in terms of computational time. TWDTW achieved comparable classification results to RF in Romania and Italy, but RF achieved better results in the USA, where the classified crops present high intra-class spectral variability. Additionally, TWDTW proved to be less sensitive in relation to the training samples. This is an important asset in areas where inputs for training samples are limited.