Apps bought on Google Play can be used on any Android device without paying again. However, each device must have the same Google Account on it. Once a purchase has been made, it may be restored to any other other device. The only proviso is that they must use the same Google or Apple account.
Android purchases may be restored on a second device by tapping the Restore button in the action bar, as shown in the screenshot on the right. The process is more or less identical for iOS devices.