There are several different screens you may have on your smartphone depending on its operating system: a home screen of static app icons, a contextual home screen, a lock screen, app drawers, and the all important notification screen. I think the notification screen is fast becoming the most important and most used screen on our mobile devices. I find it much more useful than the iPhone's grid of app icons or the stock Android home screen, which basically just provides quick access to Google searches.
I subconsciously realized this months ago when I switched to Android and no longer had a built-in way to get notifications on the lock screen, which is the default for Apple devices. I quickly found a free app that accomplished the task, and then used the app as a widget on my home screen to see all of my notifications there as well.
VC Fred Wilson recently wrote a blog post about how he uses several different messaging apps with different people and keeps it all straight through the notification center. I find myself doing the same, I'm navigating my many apps through the notification screen, not through the home screen. This is only going to get better once iOS 8 is introduced this fall, which will add widgets and actions to items in the notification center.
This leads me to an open question: why not make the notification center the default home screen on Apple and Android devices? The only information displayed on my iPhone's home screen is the date and showing which apps (of the relative few that fit on my home screen) have unread notifications. The notification center or today view would provide much more information and a quicker way to navigate through the mass of apps we all use. I swipe down just about every time I unlock my phone, why not just have that information right there on the home screen?