Images are now one of the most common form of content shared in online user-contributed sites and social Web 2.0 applications. In this paper, we present an extensive study exploring privacy and sharing needs of users' uploaded images. We develop learning models to estimate adequate privacy settings for newly uploaded images, based on carefully selected image-specific features. We focus on a set of visual-content features and on tags. We identify the smallest set of features, that by themselves or combined together with others, can perform well in properly predicting the degree of sensitivity of users' images. We consider both the case of binary privacy settings (i.e. public, private), as well as the case of more complex privacy options, characterized by multiple sharing options. Our results show that with few carefully selected features, one may achieve extremely high accuracy, especially when high-quality tags are available.