Apple debuted Notification Center feature in OS X 10.7 Lion and in OS X 10.9 Mavericks added a “Do Not Disturb” feature. If you’re busy and annoyed by the alerts popping up on the screen, you can disable them by clicking on the Notification Center icon on top-right corner, and then click to toggle on the “Do Not Disturb” switch.
A shortcut to achieve the same is to Option-click on the Notification Center icon. This however is only temporary and Notification Center will resume automatically the following day.
The only way to disable Notification Center permanently is to hack into OS X and disable the daemon from running. This is not the recommended approach if you’re not technically savvy with running command lines.
You can effectively turn off notifications using the “Do Not Disturb” schedule settings. Under Notifications system preferences, you can setup a period when “Do Not Disturb” is active. Set the time frame for example from 5 a.m. to 4.59 a.m. and OS X will then only have Notification Center enabled for that one minute.
Many are upset when Apple introduced Notifications Center to OS X, as people are just not accustom to the desktop being a notification device. Notifications on the desktop is here to stay as OS X services and apps are progressively using Notification Center more. It might not be a good idea to turn it off completely in the long run, as you may miss important system notices.