How can I turn off the home screen preview of SMS/text messages?
You may not want to see the little preview of text messages that turn up on your home screen when a new text (SMS) message comes in. To turn this off, head to your iPhone settings and go to:
iOS 7/8 UPDATE: Turn off text message, SMS and iMessage previews in alerts, banners and Notification Center with the following setting:
Settings -> Notifications -> Messages -> Show Previews -> OFF (gray switch, NOT green)
Turning off 'Show Previews' will disable the text message preview on your iPhone.