Vehicles' trajectory prediction is a topic with growing interest in recent years, as there are applications in several domains ranging from autonomous driving to traffic congestion prediction and urban planning. Predicting trajectories starting from Floating Car Data (FCD) is a complex task that comes with different challenges, namely Vehicle to Infrastructure (V2I) interaction, Vehicle to Vehicle (V2V) interaction, multimodality, and generalizability. These challenges, especially, have not been completely explored by state-of-the-art works. In particular, multimodality and generalizability have been neglected the most, and this work attempts to fill this gap by proposing and defining new datasets, metrics, and methods to help understand and predict vehicle trajectories. We propose and compare Deep Learning models based on Long Short-Term Memory and Generative Adversarial Network architectures; in particular, our GAN-3 model can be used to generate multiple predictions in multimodal scenarios. These approaches are evaluated with our newly proposed error metrics N-ADE and N-FDE, which normalize some biases in the standard Average Displacement Error (ADE) and Final Displacement Error (FDE) metrics. Experiments have been conducted using newly collected datasets in four large Italian cities (Rome, Milan, Naples, and Turin), considering different trajectory lengths to analyze error growth over a larger number of time-steps. The results prove that, although LSTM-based models are superior in unimodal scenarios, generative models perform best in those where the effects of multimodality are higher. Space-time and geographical analysis are performed, to prove the suitability of the proposed methodology for real cases and management services.