This paper studies the distributed rendezvous problem of multi-agent systems with novel event-triggered controllers. We have proposed a combinational measurement approach to event design and developed the basic event-triggered control algorithm. As a result, control of agents is only triggered at their own event time, which reduces the amount of communication and lowers the frequency of controller updates in practice. Furthermore, based on the convergence analysis of the basic algorithm, we have proposed a new iterative event-triggered algorithm where continuous measurement of the neighbor states is avoided. It is noted that the amount of communication among agents has been significantly reduced without obvious negative effects on the control performances. The effectiveness of the proposed strategies is illustrated by numerical examples in 3D spaces.