If you have a Mac and use an iOS device, Apple just announced a nice feature to go along with its new version of OS X: the ability to push iOS notifications directly to your Mac, regardless of whether or not Safari is open. The alerts show up as a banner in the top right corner of your display, much the same as any other Mac-related banner; additionally, any missed notifications will pop up in your lock screen any time you wake up your device.
Gallery: WWDC 2013: OS X Mavericks Notifications