The parsec-scale radio properties of blazars detected by the Large Area Telescope (LAT) on board the Fermi Gamma-ray Space Telescope have been investigated using observations with the Very Long Baseline Array (VLBA). Comparisons between LAT and non-LAT detected samples were made using contemporaneous data. In total, 232 sources were used in the LAT-detected sample. This very large, radio flux-limited sample of active galactic nuclei (AGN) provides insights into the mechanism that produces strong gamma-ray emission. It has been found that LAT-detected BL Lac objects are very similar to the non-LAT BL Lac objects in most properties, although LAT BL Lac objects may have longer jets. The LAT flat spectrum radio quasars (FSRQs) are significantly different from non-LAT FSRQs and are likely extreme members of the FSRQ population. Contemporaneous observations showed a strong correlation, whereas no correlation is found using archival radio data. Most of the differences between the LAT and non-LAT populations are related to the cores of the sources, indicating that the gamma-ray emission may originate near the base of the jets (i.e., within a few pc of the central engine). There is some indication that LAT-detected sources may have larger jet opening angles than the non-LAT sources. Strong core polarization is significantly more common among the LAT sources, suggesting that gamma-ray emission is related to strong, uniform magnetic fields at the base of the jets of the blazars. Observations of sources in two epochs indicate that core fractional polarization was higher when the objects were detected by the LAT. Included in our sample are several non-blazar AGN such as 3C84, M82, and NGC 6251.