A network-wide broadcast service is often used for information dissemination in sensor networks. Sensor networks are typically energy-constrained and prone to failures. In view of these constraints, the broadcast service should minimize energy consumption by reducing redundant transmissions, and be tolerant to frequent node and link failures. We propose "Smart Gossip", a probabilistic protocol that offers a broadcast service with low overheads. Smart gossip automatically and dynamically adapts transmission probabilities based on the underlying network topology. The protocol is capable of coping with wireless losses and unpredictable node failures that affect network connectivity over time. The resulting protocol is completely decentralized. We present thorough experimental results to evaluate our "Smart Gossip" proposal, and demonstrate its benefits over existing protocols.