In this paper, we investigate adaptive power allocation for generalized polar optical wireless communications (OWC), where a general complex bipolar signal is converted into magnitude and phase signals for intensity modulation. Mean square errors (MSE) between the input complex signals and the re-constructed complex signals are derived to characterize signal distortion. Optimal power scaling factors and power allocation are investigated to minimize the distortion. Under a sole average intensity constraint, closed-form optimal power scaling factors are derived and found to be input-dependent. Specifically, they are determined by the first and second moments of the magnitude signals, the first moment of the phase signals as well as the channel state. Under both average and peak intensity constraints, the expression of MSE regarding the power scaling factors is derived but it is too complicated to find the optimal power allocation. Thus, we propose to use a small-scale numerical search for practical power allocation. As an example, we adopt the proposed power allocation to polar optical orthogonal frequency division multiplexing (P-OFDM) systems and analyze its achievable bit error rate (BER). Numerical simulations are presented to validate the analysis. It is shown that the proposed power allocation greatly improves the performance in terms of MSE and BER and the proposed power allocation-enhanced P-OFDM (EP-OFDM) outperforms existing optical OFDM schemes over various channels in the high signal-to-noise ratio (SNR) regime, especially in the systems with a peak intensity constraint.