If you’re like me, since you’ve upgrade your Mac to Mountain Lion, even the default four seconds that a notification remains on the screen can bug you. You could disable notifications entirely, or even for a period of time, but that might be too extreme for your situation. Instead, to get rid of a single alert immediately, do a two-fingered swipe on the alert banner, from left to right, and it will disappear from the screen.
This assumes that you have a trackpad, although Lifehacker points out that a single-finger swipe will work with a Magic Mouse. And, as OS X Daily points out, this doesn’t close the notification, but instead moves it off of the desktop.