In classical information and communication theory, channel capacity and achievable rate over Gaussian channels, whether for constant or fading channels and whether for single user or multiple users, are characterized as functions of the power that is used for the transmission of the information. The associated circuit power that is needed in real communication transceivers to power up the electronics and to do all required signal processing is typically not involved in the capacity characterization. However, to achieve global energy efficiency of the communication systems, the adaptation of the communication schemes should be based on total power consumption. In this paper, we characterize the maximum achievable rates over many fundamental channels taking total power constraints into considerations.