Vehicular Ad Hoc Network (VANET) is an emerging field of technology that allows vehicles to communicate together in the absence of fixed infrastructure. The basic premise of VANET is that in order for a vehicle to detect other vehicles in the vicinity. This cognizance, awareness of other vehicles, can be achieved through beaconing. In the near future, many VANET applications will rely on beaconing to enhance information sharing. Further, the uneven distribution of vehicles, ranging from dense rush hour traffic to sparse late night volumes creates a pressing need for an adaptive beaconing rate control mechanism to enable a compromise between network load and precise awareness between vehicles. To this end, we propose an intelligent Adaptive Beaconing Rate (ABR) approach based on fuzzy logic to control the frequency of beaconing by taking traffic characteristics into consideration. The proposed ABR considers the percentage of vehicles traveling in the same direction, and status of vehicles as inputs of the fuzzy decision making system, in order to tune the beaconing rate according to the vehicular traffic characteristics. To achieve a fair comparison with fixed beaconing schemes, we have implemented ABR approach in JIST/SWANs. Our simulation shows that the proposed ABR approach is able to improve channel load due to beaconing, improve cooperative awareness between vehicles and reduce average packet delay in lossy/lossless urban vehicular scenarios.