The mechanism that drives the regular beating of individual cilia and flagella, as well as dense ciliary fields, remains unclear. We describe a minimal model system, composed of microtubules and molecular motors, which self-assemble into active bundles exhibiting beating patterns reminiscent of those found in eukaryotic cilia and flagella. These observations suggest that hundreds of molecular motors, acting within an elastic microtubule bundle, spontaneously synchronize their activity to generate large-scale oscillations. Furthermore, we also demonstrate that densely packed, actively bending bundles spontaneously synchronize their beating patterns to produce collective behavior similar to metachronal waves observed in ciliary fields. The simple in vitro system described here could provide insights into beating of isolated eukaryotic cilia and flagella, as well as their synchronization in dense ciliary fields.