Notice this on a regular basis in myself. Think it's really part of the human condition. We all experience it in different ways to different degrees. I woke up in the middle of the night the other night and my mind kicked into gear instantly like a screaming locomotive in my brainspace. I noticed it almost instantly. "Yo what the hell. Chill out, brain."
To get my my mind to quiet down I find it helpful to spend time doing things that intentionally get me out of my monkey mind. Meditation, play (whatever you consider play), exercise. Getting 'space' from myself. Basic stuff, but it really has a profound effect.
RE: Who else has a brain that won't shut up?