Maritime traffic is increasing more and more, creating more complex navigation environments for ships. Ship trajectory prediction based on historical AIS data is a vital method of reducing navigation risks and enhancing the efficiency of maritime traffic control. At present, employing machine learning or deep learning techniques to construct predictive models based on AIS data has become a focal point in ship trajectory prediction research. This paper systematically evaluates various trajectory prediction methods, spanning classical machine learning approaches and emerging deep learning techniques, to uncover their respective merits and drawbacks. In this work, a variety of studies were investigated that applied different algorithms in ship trajectory prediction, including regression models (RMs), artificial neural networks (ANNs), Kalman filtering (KF), and random forests (RFs) in machine learning, along with deep learning such as convolutional neural networks (CNNs), recurrent neural networks (RNNs), long short-term memory (LSTM), gate recurrent unit (GRU) networks, and sequence-to-sequence (Seq2seq) networks. The performance of predictive models based on different algorithms in trajectory prediction tasks was graded and analyzed. Among the existing studies, deep learning methods exhibit significant performance and considerable potential application value for maritime traffic systems, which can be assessed by future work on ship trajectory prediction research.