Optical interconnects have attracted considerable attention for use in short-reach communication links within high performance electronic systems, such as data centres, supercomputers and data storage systems. Multimode polymer waveguides in particular, constitute an attractive technology for use in board-level interconnects as they can be cost-effectively integrated onto standard PCBs and allow system assembly with relaxed alignment tolerances. However, their highly-multimoded nature raises important concerns about their bandwidth limitations and their potential to support very high on-board data rates. In this paper, we report record error-free (BER<10-12) 40 Gb/s data transmission over a 1 m long multimode polymer spiral waveguide and present thorough studies on the waveguide bandwidth performance. The frequency response of the waveguide is investigated under a wide range of launch conditions and in the presence of input spatial offsets which are expected to be highly-likely in real-world systems. A robust bandwidth performance is observed with a bandwidth-length product of at least 35 GHz×m for all launch conditions studied. The reported results clearly demonstrate the potential of this technology for use in board-level interconnects, and indicate that data rates of at least 40 Gb/s are feasible over waveguide lengths of 1 m.