In the present study, the capacity of two commercial NiTi and NiTiCu shape memory alloy (SMA) wires to develop work-generating (WG) and constrained-recovery (CR) shape memory effects (SMEs), as well as the capacity of a commercial NiTiFe super-elastic wire to act as cold-shape restoring element, have been investigated. Using differential scanning calorimetry (DSC), the reversible martensitic transformation to austenite of the three NiTi-based wires under study was emphasized by means of an endothermic minimum of the heat flow variation with temperature. NiTi and NiTiCu wire fragments were further tested for both WG-SME and CR-SME developed during the heating, from room temperature (RT) to different maximum temperatures selected from the DSC thermograms. The former tests revealed the capacity to repetitively lift various loads during repetitive heating, while the latter tests disclosed the repetitive development of shrinkage stresses during the repetitive heating of elongated wires. The tensile behavior of the three NiTi-based SMA wires was analyzed by failure and loading–unloading tests. The study disclosed the actuation capacity of NiTi and NiTiCu shape memory wires, which were able to develop work while being heated, as well as the resetting capacity of NiTiFe super-elastic wires, which can restore the initial undeformed shape of shape memory wires which soften while being cooled down. These features enable the design of a robotic gripper based on the development of NiTi-based actuators with repetitive action.