I found some instructions on HP to help with this kind of problem, but please read the note at the bottom of this message, as it might not be possible to turn off the notifications. =\
1 Click the "Start" menu and open the Control Panel.
2 Double click the "Printers and Faxes" icon (in Windows XP) or the "Printers" icon (in Windows Vista or later).
3 Press the "Alt" key on your keyboard to display the menu bar (Windows Vista users only).
4 Click the "File" menu and choose the "Server Properties" option.
5 Open the "Advanced" tab.
6 Uncheck the box labeled "Notify when remote documents are printed."
7 Uncheck the box labeled "Show informational notifications for local printers."
8 Uncheck the box labeled "Show informational notifications for network printers."
9 Click "OK."
Note: Keep in mind that this will not turn off essential printer messages, notifying you of problems such as lack of ink or paper jams; it turns off messages notifying you of the completion of a print job or low ink warnings. Essential printer messages are built into the firmware of the printer itself and cannot be disabled.
Oh, and this is the correct location for this kind of stuffs.