User profiling using big data raises critical issues regarding personal data and privacy. Until recently, privacy studies were focused on the control of personal data; due to big data analysis, however, new privacy issues have emerged with unidentified implications. This paper identifies and investigates privacy threats that stem from data-driven profiling using a multi-level approach: individual, group and society, to analyze the privacy implications stemming from the generation of new knowledge used for automated predictions and decisions. We also argue that mechanisms are required to protect the privacy interests of groups as entities, independently of the interests of their individual members. Finally, this paper discusses privacy threats resulting from the cumulative effect of big data profiling.