Event-triggered control aims at reducing the communication load over the feedback link in networked control systems by adapting the information exchange to the current needs. This paper firstly extends a common approach to event-triggered control by incorporating a PI controller and by showing the setpoint-tracking properties of the extended scheme. Second, it investigates the consequences of actuator saturation on the behavior of the event-triggered PI-control loop. Simulations show that the effect of actuator saturation depends on the selection of the event threshold which might even destabilize the closed-loop system due to integrator windup. Finally anti-windup techniques are discussed to overcome this problem.