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Emerging applications rely on wireless broadcast to disseminate time-critical information. For example, vehicular networks may exchange vehicle position and velocity information to enable safety applications. The number of nodes in one-hop communication range in such networks can be very large, leading to congestion and undesirable levels of packet collisions. Earlier work has examined such broadcasting protocols primarily from a MAC perspective and focused on selective aspects such as packet error rate. In this work, we propose a more comprehensive metric, the average system information age, which captures the requirement of such applications to maintain current state information from all other nearby nodes. We show that information age is minimized at an optimal operating point that lies between the extremes of maximum throughput and minimum delay. Further, while age can be minimized by saturating the MAC and setting the CW size to its throughput-optimal value, the same cannot be achieved without changes in existing hardware. Also, via simulations we show that simple contention window size adaptations like increasing or decreasing the window size are unsuitable for reducing age. This motivates our design of an application-layer broadcast rate adaptation algorithm. It uses local decisions at nodes in the network to adapt their messaging rate to keep the system age to a minimum. Our simulations and experiments with 300 ORBIT nodes show that the algorithm effectively adapts the messaging rates and minimizes the system age.