Here's an example of what I'm talking about:
On an iPhone, you can set this to come up in the lock screen and in the home screen. You can set it up to banner flash, or a notification like shown above.
Perfect example of why I would like this. Just now, my Note 2 made the Sportscenter notification sound, but other than that it did nothing else. It didn't flash the screen on for a few seconds, there is no notification LED, basically nothing to tell me that something is happening other than the audible tone. Even when I unlock the phone, the only thing I see is the SC logo in the notifications area, and I still have to scroll down to see it.
Is there something that is similar to this in Android through the settings without having to load a widget? I tried the Sportscenter widget and it doesn't update with the scores, it just shows when the next game is.