When I have apps that need updating in OSX I get a notification on the top-right corner of my screen that does not go away until I click it (which opens the app-store). Is there a way to turn these notifications off?
If the App store doesn't know about updates it should not be able to notify you - so within System Preferences go into the "App Store" preference pane and deactivate the option to search for updates automatically.
In OSX Mavericks:
You can temporarily disable the notifications by scrolling down in your notifications panel and switching the "Do Not Disturb" to On. My understanding is that the duration of time that this is in effect is determined by your settings in System Preferences > Notifications > Do Not Disturb > From XXX to XXX.