When scrolling down page and reading posts, it'd be nice to see the StackExchange notifications so as to not scroll up to top to see if I have new messages -- similar to how some social sharing tools will move from the top of the article to the white space left of page content and scroll down with you.
I don't mean having the top navigation being sticky/frozen at the top. I mean move some key notifications to the empty white space outside of site content, if your window is wide enough. Also not talking about extra scripts, browser add-ons, hitting the home button etc. I just mean simple, unobtrusive way to see notifications when you are reading other content and don't want to scroll away.
UPDATE: After implementing this answer from a previous post and changing style to look like my mockup below, the result was a little annoying when the box was always there. Amending this feature request to suggest that the StackExchange box would only appear on the left when you have a new notification, otherwise you don't see it. So if you get a new message while reading, it would fade-in and you could click to read it without having to scroll away from your content.