This paper analyzes the response of Langmuir probes to periodic or random fluctuations in plasmas with the specific aim of developing methods for measuring statistical properties of unsteady or turbulent electron-rich gases. Beginning with the classical theory of Langmuir and Mott-Smith for the probe steady-state characteristics, the waveform-independent effect of fluctuations in the electron density and temperature and the plasma potential is found on the response of plane, cylindrical, and spherical probes operating with positive or negative bias. Relations are derived showing the effect of fluctuations on the average current, as well as formulas connecting the fluctuations and the rms. probe current. It is found that the average current of the positive cylindrical probe is independent of fluctuations of any magnitude and that the electron density fluctuations can be easily measured with this probe. Experiments were performed in a low-density flowing argon plasma with fine cylindrical tungsten wires during which both the average and rms. probe current were measured. Relevant features of the theory were verified, and fluctuations were measured quantitatively.