Existing location-based services provide specialized services to their customers based on the knowledge of their exact locations. With untrustworthy servers, location-based services may lead to several privacy threats ranging from worries over employers snooping on their workers' whereabouts to fears of tracking by potential stalkers. While there exist several techniques to preserve location privacy in mobile environments, these techniques are limited as they do not distinguish between location privacy (i.e., a user wants to hide her location) and query privacy (i.e., a user can reveal her location but not her query). This distinction is crucial in many applications where the locations of mobile users are publicly known. In this paper, we go beyond the limitation of existing cloaking algorithms as we propose a new robust spatial cloaking technique for snapshot and continuous location-based queries that clearly distinguishes between location privacy and query privacy. By this distinction, we achieve two main goals: (1) supporting private location-based services to those customers with public locations, and (2) performing spatial cloaking on-demand basis only (i.e., when issuing queries) rather than exhaustively cloaking every single location update. Experimental results show that the robust spatial cloaking algorithm is scalable and efficient while providing anonymity for large numbers of continuous queries without hiding users' locations.