Beginning with Adobe Acrobat Reader X, the option to disable update notifications has been removed from the program's settings. Update notifications are now being managed by a separated service called the Adobe Acrobat Update Service. This guide explains how to stop Adobe Acrobat Reader from displaying pesky notifications on your desktop.
How To Turn Off the Adobe Acrobat Update Service
Open the Run command, type
and press Enter:
Clear the Adobe Acrobat Update Service checkbox and click on Apply > OK: