We devised a controlled hydrogen plasma reaction at 300 degrees C to etch graphene and graphene nanoribbons (GNRs) selectively at the edges over the basal plane. Atomic force microscope imaging showed that the etching rates for single-layer and few-layer (>= 2 layers) graphene are 0.27 +/- 0.05 nm/min and 0.10 +/- 0.03 nm/min, respectively. Meanwhile, Raman spectroscopic mapping revealed no D band in the planes of single-layer or few-layer graphene after the plasma reaction, suggesting selective etching at the graphene edges without introducing defects in the basal plane. We found that hydrogen plasma at lower temperature (room temperature) or a higher temperature (500 degrees C) could hydrogenate the basal plane or introduce defects in the basal plane. Using the hydrogen plasma reaction at the intermediate temperature (300 degrees C), we obtained narrow, presumably hydrogen terminated GNRs (sub-5 nm) by etching of wide GNRs derived from unzipping of multiwalled carbon nanotubes. Such GNRs exhibited semiconducting characteristics with high on/off ratios (similar to 1000) in GNR field effect transistor devices at room temperature.