I've gone through the settings menu but can only find options to change the vibration pattern, not to turn it off completely. Any ideas??
On my Samsung Galaxy S3, this setting is inside the Text Messaging app, rather than as a general setting.
Open the Text Messaging app, and start the Settings menu.
About halfway down I have a block of Notification settings.
First being Notifications,
Second being Ringtone,
Third is Vibrate.
Uncheck and you're done.
Hope your Settings Menu is similar since its from the Samsung family.