A harvesting system for harvesting stalky plants is mountable on a power unit such as an agricultural or construction tractor having hydraulic power and/or a power takeoff (PTO). The system includes at least a reel-based harvesting head configured to cut off at least the tops of the plants and to transport the cut plants laterally of the harvesting system without threshing or otherwise processing the plants. The harvesting head may be mounted on, for example, an upper lift arm assembly or a three-point hitch mechanism of the power unit. If the harvesting head is mounted on the upper lift arm assembly of an agricultural tractor, a second harvesting head may be mountable on the tractor's three-point hitch mechanism beneath the first harvesting head for cutting stalks near their base, gathering the cut stalks, and windrowing the cut stalks behind the second harvesting head.
