Press Alt+V to toggle the notifications on and off.
Personally I like to keep them on.
EDIT:
I'll also give you more info about the ALT commands on battle.net
If you look at the buttons on the interface such as QUIT, LADDER, JOIN, CHANNEL, FRIENDS you will see one letter is underlined.
If you press ALT+ underlined letter it is an alternative to pressing the button.
Also if you highlight someone's name in the channel list on the right and press ALT+N it will copy the person's name to the text box so you don't have to always type someone's account out.