In Webmail you can turn off the "You've Got Mail" message by going into Settings and unchecking "Play a sound when new mail arrives" under the General section.
In AOL versions 9.0 and 9.1 you can disable the message by going into Mail Setting under the Mail menu. Once there, click on the Advanced tab and then uncheck the “Play sound when new mail is delivered” setting.
In AOL Desktop click on the Help drop down menu in the upper right-hand corner and select Settings. Under the Mail tab in the Notifications section you can change your settings as desired.