Cybercriminals pose a significant threat to blockchain trading security, causing $40.9 billion in losses in 2024. However, the lack of an effective real-world address dataset hinders the advancement of cybercrime detection research. The anti-cybercrime efforts of researchers from broader fields, such as statistics and artificial intelligence, are blocked by data scarcity. In this paper, we present Real-CATS, a Real-world dataset of Cryptocurrency Addresses with Transaction profileS, serving as a practical training ground for developing and assessing detection methods. Real-CATS comprises 103,203 criminal addresses from real-world reports and 106,196 benign addresses from exchange customers. It satifies the C3R characteristics (Comprehensiveness, Classifiability, Customizability, and Real-world Transferability), which are fundemental for practical detection of cryptocurrency cybercrime. The dataset provides three main functions: 1) effective evaluation of detection methods, 2) support for feature extensions, and 3) a new evaluation scenario for real-world deployment. Real-CATS also offers opportunities to expand cybercrime measurement studies. It is particularly beneficial for researchers without cryptocurrency-related knowledge to engage in this emerging research field. We hope that studies on cryptocurrency cybercrime detection will be promoted by an increasing number of cross-disciplinary researchers drawn to this versatile data platform. All datasets are available at https://github.com/sjdseu/Real-CATS