Multi-channel (MC) optical wireless communication (OWC) systems employing wave-division multiplexing for outdoors free-space optical communications, or multi-user timedivision multiple access for indoors visible-light communications, e.g., can be modeled as parallel channels. Multi-input multioutput OWC systems can also be transformed, possibly with some performance loss, to parallel channels using pre-/postcoding. Studying the performance of such MC-OWC systems requires characterizing the capacity of the underlying parallel channels. In this paper, upper and lower bounds on the capacity of constant parallel OWC channels with a total average intensity constraint are derived. Then, the paper focuses on finding intensity allocations that maximize the lower bounds given channel-state information at the transmitter (CSIT). Due to its nonconvexity, the KKT conditions are used to describe a list of candidate allocations. Instead searching exhaustively for the best solution, low-complexity near-optimal algorithms are proposed. The resulting optimized lower bound nearly coincides with capacity at high signal-to-noise ratio (SNR). Under a quasi-static channel model and in the absence of CSIT, outage probability upper and lower bounds are derived. Those bounds also meet at high SNR, thus characterizing the outage capacity in this regime. Finally, the results are extended to a system with both average and peak intensity constraints.