Pulsar polarization profiles form a very basic database for understanding the emission processes in a pulsar magnetosphere. After careful polarization calibration of the 19-beam L-band receiver and verification of beam-offset observation results, we obtain polarization profiles of 682 pulsars from observations by the Five-hundred-meter Aperture Spherical radio Telescope (FAST) during the Galactic Plane Pulsar Snapshot survey and other normal FAST projects. Among them, polarization profiles of about 460 pulsars are observed for the first time. The profiles exhibit diverse features. Some pulsars have a polarization position angle curve with a good S-shaped swing, some with orthogonal modes; some have components with highly linearly polarized components or strong circularly polarized components; some have a very wide profile, coming from an aligned rotator, and some have an interpulse from a perpendicular rotator; some wide profiles are caused by interstellar scattering. We derive geometric parameters for 190 pulsars from the S-shaped position angle curves or with orthogonal modes. We find that the linear and circular polarization or the widths of pulse profiles have various frequency dependencies. Pulsars with a large fraction of linear polarization are more likely to have a large Edot.