This paper addresses the inherent technological conflict between the desire for privacy by World Wide Web users, and the need of Web content providers and advertisers to more fully collect and utilize data about users. As the other papers in this volume illustrate, the Data Mining community has now turned its collective attention towards the Web as a fertile venue for research and development. In doing so, Data Miners have found themselves at the nexus of this conflict. We present the technical issues regarding privacy from two perspectives. First, from the perspective of the Web user who may be unaware of the degree to which identifying information can be inadvertently disclosed. And second, from the perspective of a Data Miner we consider the extent to which privacy enhancing technologies could substantially invalidate data mining results.