Recently, the power consumption of integrated circuits has been attracting increasing attention. Many techniques have been studied to improve the power efficiency of digital signal processing units such as fast Fourier transform (FFT) processors, which are popularly employed in both traditional research fields, such as satellite communications, and thriving consumer electronics, such as wireless communications. This paper presents solutions based on parallel architectures for high throughput and power efficient FFT cores. Different combinations of hybrid low-power techniques are exploited to reduce power consumption, such as multiplierless units which replace the complex multipliers in FFTs, low-power commutators based on an advanced interconnection, and parallel-pipelined architectures. A number of FFT cores are implemented and evaluated for their power/area performance. The results show that up to 38% and 55% power savings can be achieved by the proposed pipelined FFTs and parallel-pipelined FFTs respectively, compared to the conventional pipelined FFT processor architectures.