Corn and soybeans are crucial crops for feeding the world's population, and it is essential to monitor and map these fields for effective agricultural planning. With recent advancements in remote sensing technology and deep learning algorithms, more intelligent management of these crops has become possible. In this paper, we compare modern deep learning (DL) architectures for mapping corn and soybean crops in the state of Iowa, in the United States of America (USA), using temporal Landsat 8 (OLI) images. Our analysis focuses on the performance of six different DL networks, namely 1-D CNN, 1-D CNN-LSTM, 2-D UNet, 2D UNet 3+, 2D Attention UNet, and 2D Recurrent Residual UNet. For each network, we use time-series Normalized Difference Vegetation Index (NDVI) data derived from Landsat 8 images taken between April and November 2020 as input, while ground truth labels are taken from the United States Department of Agriculture (USDA). Our experimental results show that the 2-D Recurrent Residual U-net model achieved the highest accuracy for identifying corn and soybean classes, with an F-score of 92.85. This indicates the model's ability to distinguish complex features and patterns with similar spectral characteristics from multi-temporal remote sensing data. Conversely, the CNN and CNN-LSTM models had the worst performance among the considered models, with an F-score of about 89.50. Nevertheless, all the DL methods examined in this study achieved acceptable classification kappa coefficients (above 82%), indicating their significant potential for accurate mapping and monitoring Corn and Soybean crops.