We have completed a spectroscopic survey of X-ray point sources in eight low-redshift clusters of galaxies (0.05 < z < 0.31) and have identified 40 cluster members with broadband (0.3-8 keV) X-ray luminosities between L_X = 8 x 10~(40) and 4 x 10~(43) ergs s~(-1). There are between two and 10 X-ray sources per cluster. We use visible-wavelength emission lines, X-ray spectral shapes, and multiwavelength flux ratios to determine that at least 35 of these galaxies are active galactic nuclei (AGNs). From our spectroscopic survey of other candidate cluster members we estimate that the AGN fraction f_A is ～5% for cluster galaxies more luminous than M_R = -20 mag hosting AGNs with broadband X-ray luminosities above L_X = 10~(41) ergs s~(-1), or f_A(M_R < -20; L_X > 10~(41)) ～ 5%. We stress that additional, lower luminosity AGNs are expected to be present in the M_r < -20 mag cluster members. Our data unambiguously demonstrate that cluster galaxies host AGNs more frequently than previously expected. Only four of these galaxies have obvious visible-wavelength AGN signatures, even though their X-ray luminosities are too high for their X-ray emission to be due to populations of low-mass X-ray binaries or hot, gaseous halos. We attribute the significant difference in visible and X-ray AGN identification to dilution of low-luminosity AGN spectral signatures by host galaxy starlight and/or obscuration of accretion onto the central, supermassive black hole.
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