Accurate crop type maps play an important role in food security due to their widespread applicability. Optical time series data (TSD) have proven to be significant for crop type mapping. However, filling in missing information due to clouds in optical imagery is always needed, which will increase the workload and the risk of error transmission, especially for imagery with high spatial resolution. The development of optical imagery with high temporal and spatial resolution and the emergence of deep learning algorithms provide solutions to this problem. Although the one-dimensional convolutional neural network (1D CNN), long short-term memory (LSTM), and gate recurrent unit (GRU) models have been used to classify crop types in previous studies, their ability to identify crop types using optical TSD with missing information needs to be further explored due to their different mechanisms for handling invalid values in TSD. In this research, we designed two groups of experiments to explore the performances and characteristics of the 1D CNN, LSTM, GRU, LSTM-CNN, and GRU-CNN models for crop type mapping using unfilled Sentinel-2 (Sentinel-2) TSD and to discover the differences between unfilled and filled Sentinel-2 TSD based on the same algorithm. A case study was conducted in Hengshui City, China, of which 70.3% is farmland. The results showed that the 1D CNN, LSTM-CNN, and GRU-CNN models achieved acceptable classification accuracies (above 85%) using unfilled TSD, even though the total missing rate of the sample values was 43.5%; these accuracies were higher and more stable than those obtained using filled TSD. Furthermore, the models recalled more samples on crop types with small parcels when using unfilled TSD. Although LSTM and GRU models did not attain accuracies as high as the other three models using unfilled TSD, their results were almost close to those with filled TSD. This research showed that crop types could be identified by deep learning features in Sentinel-2 dense time series images with missing information due to clouds or cloud shadows randomly, which avoided spending a lot of time on missing information reconstruction.