A simple setting hidden in a not-so-obvious place
Update: To clarify, this is for the international GS4 only. Looks like the US versions don't require any extra steps to enter mute mode.
If you've got an Android 4.2 phone set to vibrate mode, notifications that would normally play a sound alert cause a vibration. On the Nexus 4 that's easily avoided by cranking the volume all the way down to the "mute" level, but on the Samsung Galaxy S4 (international version only, for some reason) the lowest level on the volume bar is 'vibrate,' not 'mute.' So how do you avoid being pestered by vibration alerts? Turns out there's a simple toggle for it, though it's tucked away in a less than obvious place.
To switch to mute mode on the Galaxy S4 and silence vibration alerts for notifications, long-press the power button and hit the "mute" button. Alternatively, "mute" is one of the options you can add to the quick settings bar in the notification shade. (Scroll to the right or expand the quick settings area if you don't see it.)
Once you're in mute mode, all incoming notification sounds and vibrations will be silenced, so you won't be bothered by email alerts in the middle of the night. To switch back, use the volume rocker or one of the other sound options in the power menu.
Hit up the Android Central forums for more Galaxy S4 discussions and questions.