The procedure below is for ArcGIS 9.3.1 or earlier versions. Starting at ArcGIS 10.0, expressions in the Calculator are created using only VBScript or a standard Python format. See Count the vertices for line or polygon features in ArcMap 10.
In Workstation ArcInfo, the COUNTVERTICES command can be used to write the number of vertices for a line or polygon feature to the attribute table. Instructions provided describe how to do the same in ArcMap.
Dim pPointCount As IPointCollection
Set pPointCount = [SHAPE]