Broadcasting is the task of sending a message from a source node to all other nodes in the network. It is frequently referred to also as data dissemination. The design of reliable and efficient broadcast protocols is a key enabler for the successful deployment of vehicular communication services. In this paper we develop the Acknowledged Broadcast from Static to highly Mobile (ABSM) protocol, a fully distributed adaptive algorithm suitable for VANETs with all mobility scenarios. ABSM automatically adjusts its behavior without keeping track of the degree of mobility sensed by the vehicle. Each node independently decides whether or not to forward a received broadcast message. Such decision is solely based on the local information that vehicles acquire from their neighborhood by means of periodic beacon messages. This guarantees ultimate scalability regardless the size of the VANET. The set of parameters in ABSM is minimal and consists only of few natural choices. In a thorough simulation-based performance evaluation, our algorithm is shown to provide higher reliability and message efficiency than existing approaches for non-safety applications.