Land cover and its change are crucial for many environmental applications. This study focuses on the land cover classification and change detection with multitemporal and multispectral Sentinel-2 satellite data. To address the challenging land cover change detection task, we rely on two different deep learning architectures and selected pre-processing steps. For example, we define an excluded class and deal with temporal water shoreline changes in the pre-processing. We employ a fully convolutional neural network (FCN), and we combine the FCN with long short-term memory (LSTM) networks. The FCN can only handle monotemporal input data, while the FCN combined with LSTM can use sequential information (multitemporal). Besides, we provided fixed and variable sequences as training sequences for the combined FCN and LSTM approach. The former refers to using six defined satellite images, while the latter consists of image sequences from an extended training pool of ten images. Further, we propose measures for the robustness concerning the selection of Sentinel-2 image data as evaluation metrics. We can distinguish between actual land cover changes and misclassifications of the deep learning approaches with these metrics. According to the provided metrics, both multitemporal LSTM approaches outperform the monotemporal FCN approach, about 3 to 5 percentage points (p.p.). The LSTM approach trained on the variable sequences detects 3 p.p. more land cover changes than the LSTM approach trained on the fixed sequences. Besides, applying our selected pre-processing improves the water classification and avoids reducing the dataset effectively by 17.6%. The presented LSTM approaches can be modified to provide applicability for a variable number of image sequences since we published the code of the deep learning models. The Sentinel-2 data and the ground truth are also freely available.