This paper investigates the design of reduced-order observers for robot manipulators. Observer stability conditions are obtained based on a Lyapunov analysis. The proposed observer is enhanced with a hybrid scheme that may adjust the gains to cope with possible unbounded velocities of the robot joints. Thanks to such hybrid strategy, the observer works accurately both for robots driven by open-loop controllers and by output feedback controllers. Numerical simulations illustrate the efficacy of the reduced-order observer in several scenarios, including a comparison with the performance of a classical full-order observer.