Calculating Date Field with today's date from datetime.date.today()?

An update Cursor will out perform the field calculator 100% of the time.

You need to write this as an expression:

import arcpy, datetime

fc = r'C:\GIS\CARGIS\SHAPES.gdb\CRASH_ON_2013'
field = "DTCARXTRCT"
exp = '''def add_date():
  import time
  return time.strftime("%Y/%m/%d")'''

arcpy.CalculateField_management(fc, field, 'add_date()',
                                'PYTHON', exp)
print 'done'

datetime.date.today() did not work in field calculator, switched to strftime.

OR, if you want to do it the better way where you can feed your own variables in, use a cursor:

import arcpy, datetime

fc = r'C:\GIS\CARGIS\SHAPES.gdb\CRASH_ON_2013'
field = "DTCARXTRCT"
with arcpy.da.UpdateCursor(fc, [field]) as rows:
    for row in rows:
        rows.updateRow([datetime.date.today()])
print 'done'