I generally keep my phone on silent, and I have significantly restricted the Notifications settings for most of my apps. I allow app badges, but only a few apps are allowed banners and sounds/vibrations.
I had just done another pass through Notifications to further restrict things, and ended up with a phantom vibration that would appear seemingly randomly on my phone. I couldn't see any other notification that it might be associated with, so it was frustratingly difficult to troubleshoot.
After searching online, I found out that Apple—for some annoying reason—has a second location in Settings for vibration alerts. It's under Sounds. There were vibrations set for Tweet and Facebook Post, as well as New Mail. I set all of these to None and now my phantom vibrations are gone.