Technically, you have to go into each shapefile separately to update it, but you could do it by running a single a Python program that loops through all the files in a directory and uses an update cursor to update the field in each one. Are your files all in a single directory? What is the name of the shared field? Anyway, the basic approach to the program is as follows, which would be run in a standalone python script:
from arcpy import env
# Set the workspace for the ListFeatureClass function
env.workspace = "c:/base"
# Use the ListFeatureClasses function to return a list of
# all shapefiles.
fcList = arcpy.ListFeatureClasses()
fields = ["MyField", "OID@", "MyOtherField"]
counter = 0
# Use an update cursor on each shapefile to update two fields
for fc in fcList:
with arcpy.da.UpdateCursor(fc, fields) as cursor:
for row in cursor:
# Example of using a counter to make every sure every value is
# unique in MyField in every shapefile.
counter += 1
row = counter
# Example of a conditional update showing that you can update
# one field based on the values contained in another field
# Also, unlike the Field Calculator, an update cursor can update
# every field in the shapefile in a single pass if you need to
if (row >= 0 and row <= 10): # ObjectID values checked
row = 1 # MyOtherField updates to 1 if it meets the condition
row = 0 # MyOtherField updates to 0 if it doesn't meet it
cursor.updateRow(row) # store the updates
If only some of the shapefiles in the directory have the field and other don't, code would have be added to check that the fields exists in the shapefile before attempting to update it. Shapefiles that don't have the field would be skipped.