For maximizing the energy efficiency in a wireless network, we propose two forwarding schemes termed single-link and multi-link energy-efficient forwarding that tradeoff delivery ratios against energy costs. Multi-link forwarding improves the network performance substantially by addressing multiple receivers at once during the packet forwarding process. If the first forwarding node does not receive a packet correctly, other nodes may act as backup nodes and perform the forwarding instead. By means of mathematical analyses, we derive how the energy efficiency of a forwarding path can be computed and how a forwarding tree is established. Routing cycles are explicitly taken into account and prevented by means of sequence numbers. Simulations and real-world experiments provide a comparison to other reference strategies, showing a superior performance of our forwarding scheme in terms of energy efficiency.