Recurrent copy number alterations (CNAs) play an important role in cancer genesis. While a number of computational methods have been proposed for identifying such CNAs, their relative merits remain largely unknown in practice since very few efforts have been focused on comparative analysis of the methods. To facilitate studies of recurrent CNA identification in cancer genome, it is imperative to conduct a comprehensive comparison of performance and limitations among existing methods. In this paper, six representative methods proposed in the latest six years are compared. These include one-stage and two-stage approaches, working with raw intensity ratio data and discretized data respectively. They are based on various techniques such as kernel regression, correlation matrix diagonal segmentation, semi-parametric permutation and cyclic permutation schemes. We explore multiple criteria including type I error rate, detection power, Receiver Operating Characteristics (ROC) curve and the area under curve (AUC), and computational complexity, to evaluate performance of the methods under multiple simulation scenarios. We also characterize their abilities on applications to two real datasets obtained from cancers with lung adenocarcinoma and glioblastoma. This comparison study reveals general characteristics of the existing methods for identifying recurrent CNAs, and further provides new insights into their strengths and weaknesses. It is believed helpful to accelerate the development of novel and improved methods.