The actin cytoskeleton is an active gel which constantly remodels during cellular processes such as motility and division. Myosin II molecular motors are involved in this active remodeling process and therefore control the dynamic self-organization of cytoskeletal structures. Due to the complexity of in vivo systems, it is hard to investigate the role of myosin II in the reorganization process which determines the resulting cytoskeletal structures. Here we use an in vitro model system to show that myosin II actively reorganizes actin into a variety of mesoscopic patterns, but only in the presence of bundling proteins. We find that the nature of the reorganization process is complex, exhibiting patterns and dynamical phenomena not predicted by current theoretical models and not observed in corresponding passive systems (excluding motors). This system generates active networks, asters and even rings depending on motor and bundling protein concentrations. Furthermore, the motors generate the formation of the patterns, but above a critical concentration they can also disassemble them and even totally prevent the polymerization and bundling of actin filaments. These results may suggest that tuning the assembly and disassembly of cytoskeletal structures can be obtained by tuning the local myosin II concentration/activity.