Natural language processing (NLP) based approaches have recently received attention for legal systems of several countries. It is of interest to study the wide variety of legal systems that have so far not received any attention. In particular, for the legal system of the Republic of Turkey, codified in Turkish, no works have been published. We first review the state-of-the-art of NLP in law, and then study the problem of predicting verdicts for several different courts, using several different algorithms. This study is much broader than earlier studies in the number of different courts and the variety of algorithms it includes. Therefore it provides a reference point and baseline for further studies in this area. We further hope the scope and systematic nature of this study can set a framework that can be applied to the study of other legal systems. We present novel results on predicting the rulings of the Turkish Constitutional Court and Courts of Appeal, using only fact descriptions, and without seeing the actual rulings. The methods that are utilized are based on Decision Trees (DTs), Random Forests (RFs), Support Vector Machines (SVMs) and state-of-the-art deep learning (DL) methods; specifically Gated Recurrent Units (GRUs), Long Short-Term Memory networks (LSTMs) and bidirectional LSTMs (BiLSTMs), with the integration of an attention mechanism for each model. The prediction results for all algorithms are given in a comparative and detailed manner. We demonstrate that outcomes of the courts of Turkish legal system can be predicted with high accuracy, especially with deep learning based methods. The presented results exhibit similar performance to earlier work in the literature for other languages and legal systems.