Network coding not only improves information flow rates in a network but shapes traffic and, hence, can induce some predictability structure on communication channels as well. Specifically, due to the buffering and batch processing involved in network coding, transitions between busy and idle periods in channel use are expected to be less frequent, which, in turn, result in a more predictable structure of network-coded communications, compared with traditional store-and-forward-based transmissions. For broadcast communications over erasure channels, we characterize how network coding adds memory to the channel use at the traffic level and increases the spectrum predictability, compared with the plain retransmission scheme. This traffic-shaping effect of network coding can be readily applied to cognitive radio networks. In particular, we develop adaptive spectrum sensing for secondary users (SUs) to exploit the induced predictability in primary user channels with network-coded transmissions and show that the throughput of SUs is significantly improved. On the other hand, we caution that the predictable structure of network-coded transmissions also makes wireless channels more susceptible to jamming attacks. Our results lead to a new understanding of network coding as a spectrum shaper and reveal the inherent tradeoffs between the throughput and security objectives resulting from the spectrum predictability induced by network coding.