A growing number of sensors, embedded in wearables, smart electric meters and other connected devices, is surrounding us and reaching ever deeper into our private lives. While some sensors are commonly regarded as privacy-sensitive and always require user permission to be activated, others are less protected and less worried about. However, experimental research findings indicate that many seemingly innocuous sensors can be exploited to infer highly sensitive information about people in their vicinity. This paper reviews existing evidence from the literature and discusses potential implications for consumer privacy. Specifically, the analysis reveals that certain insufficiently protected sensors in smart devices allow inferences about users’ locations, activities and real identities, as well as about their keyboard and touchscreen inputs. The presented findings call into question the adequacy of current sensor access policies. It is argued that most data captured by smart consumer devices should be classified as highly sensitive by default. An introductory overview of sensors commonly found in these devices is also provided, along with a proposed classification scheme.