To elucidate the origin of the 1/f fluctuations in tunneling current in scanning tunneling microscopes (STM), a systematic study was performed on combinations of Pt-Ir alloy tips and Au and graphite samples in air. The noise power increases quadratically with the tunneling current when the tunnel resistance is fixed constant, which indicates that the current fluctuations arise from the fluctuations of the tunnel resistance. The noise intensity increasing also with the tip-sample distance z rules out fluctuations of z from possible causes of the current fluctuations. Measurements of work function phi revealed a low-frequency fluctuation in phi as well. The noise power in a fixed bandwidth exhibited spatial variations on the Au surfaces, which have some correlation with the STM topography and more direct correlation with the spatial variation of phi. The experimental results are discussed in terms of desorption/adsorption of ambient gas molecules on the sample/tip surfaces.