Our smartphone is full of applications and data that analytically organize, facilitate and describe our lives. We install applications for the most varied reasons, to inform us, to have fun, for work, for necessity, but, unfortunately, we often install them without reading the terms and conditions of use. The result is that our privacy is increasingly at risk. Considering this scenario, in this paper, we analyze the user's perception towards privacy while using smartphone applications. In particular, we formulate two different hypotheses: 1) the perception of privacy is influenced by the knowledge of the data used by the installed applications; 2) applications access to much more data than they need. The study is based on two questionnaires (within-subject experiments with 200 volunteers) and on the lists of installed apps (30 volunteers). Results show a widespread abuse of data related to location, personal contacts, camera, Wi-Fi network list, running apps list, and vibration. An indepth analysis shows that some features are more relevant to certain groups of users (e.g., adults are mainly worried about contacts and Wi-Fi connection lists; iOS users are sensitive to smartphone vibration; female participants are worried about possible misuse of the smartphone camera).