Those banners are handy, as you can use them as a way to skip songs you don’t wanna hear (just hover your cursor over one to reveal the “Skip” button).
Please don't ever skip this particular song. I will judge you for it.
I like this feature a lot—a lot a lot a lot, especially since I listen to iTunes Radio and thus don’t always know what’s playing—but if you hate it, you can turn it off. There are a couple of methods for doing that, but we’re gonna look at iTunes> Preferences> General to do so, as there’s another feature under that tab that I think you’ll dig.
So that first option—“When song changes”—controls whether or not you see the pop-up notifications pictured in my first couple of screenshots. Turn that off, and they’ll stop coming. It’s the second choice listed there, though, that is really pretty awesome. If you toggle on “Keep all song changes in Notification Center,” then you can always open Notification Center to see (by default) the last five songs that’ve played.
If you click on any song within that view, you’ll be taken to where it lives in iTunes. If it was from your library, you’ll go right to the song; if it happened to be a track from iTunes Radio, clicking it will show you your history in that station (with, of course, a link to purchase what you've heard).
You can also control how many songs show up in Notification Center's history under System Preferences> Notifications> iTunes. Just change the “Show in Notification Center” drop-down to your preferred number, and you’re done.
One final thing: Keep in mind that iTunes' behavior can be overridden by settings that are within that same System Preferences> Notifications> iTunes panel. So if you’re not seeing what you expect from the program, notifications-wise, be sure to check there in case you’ve got “Show in Notification Center” toggled off or something. Which would mean that you wouldn't get any song history at all. And then you'd probably be mad at me for writing a bad tip. Let's not go down that road, OK? I'm sensitive.