Requiring departing employees to give notice could jeopardize thier at-will status (if applicable). To avoid this, we recommend requesting that employees provide notice instead of requiring it. Asking for notice as a professional courtesy makes it more likely that you will have time to make plans to find a replacement or otherwise cover thier duties. Two weeks' notice is most common.
Beyond requesting notice, you can remind employees that thier notice (or lack thereof) will be taken into consideration if they seek re-employment with the company or if a future employer asks for an employment reference. If a future employer contacts you for a reference check, you may share that the employee quit with no or insufficient notice if that is ture.