The increasing volume of remote sensing data with improved spatial and temporal resolutions generates unique opportunities for monitoring and mapping of crops. We compared multiple single-band and multi-band object-based time-constrained Dynamic Time Warping (DTW) classifications for crop mapping based on Sentinel-2 time series of vegetation indices. We tested it on two complex and intensively managed agricultural areas in California and Texas. DTW is a time-flexible method for comparing two temporal patterns by considering their temporal distortions in their alignment. For crop mapping, using time constraints in computing DTW is recommended in order to consider the seasonality of crops. We tested different time constraints in DTW (15, 30, 45, and 60 days) and compared the results with those obtained by using Euclidean distance or a DTW without time constraint. Best classification results were for time delays of both 30 and 45 days in California: 79.5% for single-band DTWs and 85.6% for multi-band DTWs. In Texas, 45 days was best for single-band DTW (89.1%), while 30 days yielded best results for multi-band DTW (87.6%). Using temporal information from five vegetation indices instead of one increased the overall accuracy in California with 6.1%. We discuss the implications of DTW dissimilarity values in understanding the classification errors. Considering the possible sources of errors and their propagation throughout our analysis, we had combined errors of 22.2% and 16.8% for California and 24.6% and 25.4% for Texas study areas. The proposed workflow is the first implementation of DTW in an object-based image analysis (OBIA) environment and represents a promising step towards generating fast, accurate, and ready-to-use agricultural data products.