To receive personalized web services, the user has to provide personal information and preferences, in addition to the query itself, to the web service. However, detailed personal information could identify the sender of sensitive queries, thus compromise user privacy. We propose the notion of online anonymity to enable users to issue personalized queries to an untrusted web service while with their anonymity preserved. The challenge for providing online anonymity is dealing with unknown and dynamic web users who can get online and offline at any time. We define this problem, discuss its implications and differences from the problems in the literature, and propose a solution. Categories and Subject Descriptors H.3.5 [Online Information Services]: Web-based services; K.4.1 [Public Policy Issues]: Privacy General Terms Algorithms, Performance, Design, Experimentation, Theory Keywords Online anonymity, web services, privacy, personalization