In this paper, the optimal power control policy that maximizes the effective capacity for arbitrary input distributions in fading channels subject to an average power constraint is studied. A low-complexity power control algorithm is proposed. In addition, energy efficiency is investigated by characterizing both the minimum energy per bit and wideband slope for arbitrary signaling in the low-power regime when channel side information (CSI) is available only at the receiver. With perfect CSI at both the transmitter and receiver, the optimal power adaptation strategy in this regime is also determined. Through numerical results, performance comparison with constant power scheme and optimal power adaptation strategy for different signal constellations and Gaussian signals is given. The impact of QoS constraints, input distributions, and average transmit power level on the proposed power control policy, maximum achievable effective capacity and energy efficiency is analyzed.