In this article, the consensus of networked underactuated robotic systems subject to fixed and switched communication networks is discussed by developing some novel event-triggered control algorithms, which can synchronously guarantee the convergence of the active states, the boundedness of the velocities of passive actuators, and the exclusion of Zeno behaviors. In the cases of fixed networks, the sufficient criteria are established for the presented distributed event-triggered mechanisms with and without using neighbors' velocities, in order to achieve a better tradeoff between the communication load and system performance. Besides, in the situation of switched networks, the sufficient criterion is established by assuming that the union of the network has a spanning tree. A distributed sampled-data rule is constructed to decide when to update its own and neighbors' estimated positions, and thus further reduces the unnecessary control cost. Finally, by further extending the main results to three other sampled-data control algorithms, several examples with performance comparisons are provided to validate the efficiency and advantages of the theoretical results.