We surveyed fast current sheet crossings (flapping motions) over the distance range 10-30 R-E in the magnetotail covered by the Geotail spacecraft. Since the local tilts of these dynamic sheets are large and variable in these events, we compare three different methods of evaluating current sheet normals using 4-s/c Cluster data and define the success criteria for the single-spacecraft-based method (MVA) to obtain the reliable results. Then, after identifying more than 1100 fast CS crossings over a 3-year period of Geotail observations in 1997-1999, we address their parameters, spatial distribution and activity dependence. We confirm that over the entire distance covered and LT bins, fast crossings have considerable tilts in the YZ plane (from estimated MVA normals) which show a preferential appearance of one (YZ kinklike) mode that is responsible for these severe current sheet perturbations. Their occurrence is highly inhomogeneous; it sharply increases with radial distance and has a peak in the tail center (with some duskward shift), resembling the occurrence of the BBFs, although there is no one-to-one local correspondence between these two phenomena. The crossing durations typically spread around 1 min and decrease significantly where the high-speed flows are registered. Based on an AE index superposed epoch study, the flapping motions prefer to appear during the substorm expansion phase, although a considerable number of events without any electrojet and auroral activity were also observed. We also present statistical distributions of other parameters and briefly discuss what could be possible mechanisms to generate the flapping motions.