We present circular polarization results from a 5 GHz survey of the parsec-scale polarization properties of 40 active galactic nuclei (AGNs) made with the VLBA. We find 11 circular polarization detections at the 3 sigma level or higher. This nearly quadruples the number of sources detected in circular polarization at VLBI resolution. We find no correlation between fractional linear and circular polarization across our sample. A likely explanation is external Faraday depolarization in the cores of AGNs which reduces linear polarization but leaves circular polarization unchanged. In comparing ours and other recent results to observations made similar to 20 years ago, we find that, in five of six cases, sources have the same sign of circular polarization today as they did 20 years ago. This suggests the presence of a long-term property of the jets, such as the polarity of a net magnetic flux, which is stable on timescales much longer than those of individual outbursts.