The leader-following attitude consensus problem of networked rigid spacecraft systems is addressed by a distributed control law. Compared with existing results, the salient characteristic of this work is that the communication network is allowed to be directed and switching. In particular, the switching network only needs to be jointly connected, which is a very mild condition on network connectivity. As a consequence, the robustness and reliability for consensus of networked rigid spacecraft systems can be greatly improved. By establishing a series of technical lemmas, it is shown that leader-following attitude consensus of switched networked rigid spacecraft systems can be achieved. The effectiveness of our main result is demonstrated by cooperative control of a group of rigid spacecraft.