Extracting coordinates of polygon vertices in ArcMap?

Use the Feature Vertices To Points tool within ArcToolbox or if you do not have Advanced license then you may use the Polygon to Point tool from ET GeoWizard (free tool). Finally, in ArcMap use the Add XY Coordinates tool to generate the XY value for each vertex and use Table to Excel to generate a spreadsheet.

This works with a standard ArcGIS license:

desc = arcpy.Describe(fcl)
shapefieldname = desc.ShapeFieldName

gebieden = arcpy.UpdateCursor(fcl)

for gebied in gebieden:
    polygoon = gebied.getValue(shapefieldname)
    for punten in polygoon:
        for punt in punten:
            print punt.X, punt.Y

There is a sample toolbox which includes a Write Features To Text File python script which:

Writes feature coordinates to a text file.

Note:

Technically, the tools in the Samples toolbox have been deprecated. They are still installed with ArcGIS so that any existing script or model tools you developed before 10 continue to work.