As the Internet struggles to cope with scalability, mobility, and security issues, new network architectures are being proposed to better accommodate the needs of modern systems and applications. In particular, Content-Oriented Networking (CON) has emerged as a promising next-generation Internet architecture: it sets to decouple content from hosts, at the network layer, by naming data rather than hosts. CON comes with a potential for a wide range of benefits, including reduced congestion and improved delivery speed by means of content caching, simpler configuration of network devices, and security at the data level. However, it remains an interesting open question whether or not, and to what extent, this emerging networking paradigm bears new privacy challenges. In this paper, we provide a systematic privacy analysis of CON and the common building blocks among its various architectural instances in order to highlight emerging privacy threats, and analyze a few potential countermeasures. Finally, we present a comparison between CON and today's Internet in the context of a few privacy concepts, such as, anonymity, censoring, traceability, and confidentiality