Jet does not support triggers so the only way to do this when your back end tables are Access, is through a form. If your backend db is something else such as SQL server, you should use a trigger. If the Audit Trail article that Jack found for you is more than you want, you can just add a new column to the table and call it LastUpdateDt. Then in the BeforeUpdate event of any form that updates the table add a single line of code:
Me.LastUpdateDt = Now()
The field does not need to be displayed on the form but it does need to be in the form's recordsource. So don't forget to add the new column to the query used as the form's recrodsource. If the form doesn't recognize the new field you will need to force the form to refresh its fields collection. To do this, delete the query name from the form's recordsource, save the form, and the just put the query name back into the recordsource.