We conducted a Very Large Array survey of 11 low-luminosity active galactic nuclei (LLAGNs) for linear and circular polarization at 8.4 GHz. We detected circular polarization in one source (M81*) and linear polarization in three sources. Sensitivity limits were similar to0.1% for both modes of polarization in nine of 11 sources. The detections confirm the importance of nonthermal emission in LLAGNs. However, detection rates for circular and linear polarization are lower for these sources than for more powerful AGNs. Fractional linear polarization in detected sources is also lower than in more powerful AGNs. The weak linear polarization in the survey sources indicates their overall similarity to Sgr A*. Confusion with thermal sources, depolarization, and weaker, less extended jets may contribute to these differences. We detect a rotation measure greater than or similar to7 x 10(4) rad m(-2) for NGC 4579. This may arise from magnetized plasma in the accretion, outflow, or interstellar regions. Inverted spectra are present in both M81* and Sgr A* and absent from all sources in which circular polarization is not detected. This suggests that optical depth effects are important in the creation of circular polarization.