In this paper, we formulate and solve a weighted-sum transmitter and receiver energy minimization (WSTREMin) problem in the downlink of an orthogonal frequency division multiplexing (OFDM) based multiuser wireless system. The proposed approach offers the flexibility of assigning different levels of importance to base station (BS) and mobile terminal (MT) power consumption, corresponding to the BS being connected to the grid and the MT relying on batteries. To obtain insights into the characteristics of the problem, we first consider two extreme cases separately, i.e., weighted-sum receiver-side energy minimization (WSREMin) for MTs and transmitter-side energy minimization (TEMin) for the BS. It is shown that Dynamic TDMA (D-TDMA), where MTs are scheduled for single-user OFDM transmissions over orthogonal time slots, is the optimal transmission strategy for WSREMin at MTs, while OFDMA is optimal for TEMin at the BS. As a hybrid of the two extreme cases, we further propose a new multiple access scheme, i.e., Time-Slotted OFDMA (TS-OFDMA) scheme, in which MTs are grouped into orthogonal time slots with OFDMA applied to users assigned within the same slot. TS-OFDMA can be shown to include both D-TDMA and OFDMA as special cases. Numerical results confirm that the proposed schemes enable a flexible range of energy consumption tradeoffs between the BS and MTs.