This paper investigates simultaneous wireless information and power transfer (SWIPT) in energy harvesting (EH) relay systems. Unlike existing SWIPT schemes requiring the channel state information (CSI) for coherent information delivery, we propose a noncoherent SWIPT framework for decode-and-forward (DF) relay systems bypassing the need for CSI and consequently saving energy in the network. The proposed SWIPT framework embraces power-splitting noncoherent DF (PS-NcDF) and time-switching noncoherent DF (TS-NcDF) in a unified form, and supports arbitrary M-ary noncoherent frequency-shift keying (FSK) and differential phase-shift keying (DPSK). Exact (noncoherent) maximum-likelihood detectors (MLDs) for PS-NcDF and TS-NcDF are developed in a unified form, which involves integral evaluations yet serves as the optimum performance benchmark for noncoherent SWIPT. To reduce the computational cost of the exact MLDs, we also propose closed-form approximate MLDs achieving near-optimum performance, thus serving as a practical solution for noncoherent SWIPT. Numerical results demonstrate a performance tradeoff between the first and second hops through the adjustment of time switching or power splitting parameters, whose optimal values minimizing the symbol-error rate (SER) are strictly between 0 and 1. We demonstrate that M-FSK results in a significant energy saving over M-DPSK for M >= 8; thus M-FSK may be more suitable for EH relay systems.