In Vehicular Ad hoc Networks (VANETs), authentication is a crucial security requirement to avoid attacks to both inter-vehicle and vehicle-roadside communication. Vehicles have to be prevented from the misuse of their private data and the attacks on their privacy. In this paper, we investigate the authentication and privacy issues in VANETs. We propose a novel ID-based authentication framework with adaptive privacy preservation for VANETs. In this framework, adaptive self-generated pseudonyms are used as identifiers instead of real-world IDs. The update of the pseudonyms depends on vehicular demands. The ID-Based Signature (IBS) scheme and the ID-Based Online/Offline Signature (IBOOS) scheme are used, for authentication between the Road Side Units (RSUs) and vehicles, as well as authentication among vehicles, respectively. System evaluation has been executed using efficient IBS and IBOOS schemes. It shows that, the proposed authentication framework with privacy preservation is suitable to the VANET environment.