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.
You can also use this screen to set other parameters for alerts, including Alert Style.