The solution is simple: If you use a trackpad, use two fingers to swipe them away to the right; on the Magic Mouse, it's one finger swipe to the right. Of course, hover over it with the cursor and then swipe.
[kirkmc adds: Well, I wasn't sure whether to post this. The banners go away on their own after five seconds, so you'd need to be mighty impatient to want to go to the trouble of manually removing them. But there may be cases where you do want to do this. I'll let you discuss this in the comments below.]

