We've all gotten text messages/iMessages from companies or people that didn't require a trumpet fanfare text tone and a violent vibration in our pocket. With iOS 7, you can now assign a contact no text sound and no vibration for a completely silent and still (non) notification. I find this useful for things like verification codes sent via SMS from places like Outlook.com, Google, Evernote, etc. or notifications from my bank, credit card company, etc.
Using this method, you can selectively decide which sender's messages get no notification.
First you'll need to save the sender as a Contact in your phone. This can be quickly done from the text message by tapping the word "Contact" in the top right corner of the message, then tap the "i" that appears and tap "Create New Contact".
Once your contact is created, you'll need to edit the Contact. If you just created the Contact and didn't tap done you're already in Edit mode. If your contact is already saved, locate the Contact and tap the word "Edit" in the top right corner.
Now scroll down to the Text Tone entry and tap to the right.
Just under your Default text tone you'll find "None" - tap this, then the word "Done" in the top right corner.
Repeat the previous step for Vibration, and you're now free from sound and vibration for that sender.
These instructions are for iPhones running iOS 7. You can do the same on iPad, however buttons may be located in a slightly different location.