You can use Chime.
It's perfect! I found it recently while browsing through the Chrome Store (because that's just what I do ;p)
- stack exchange
- google plus
You can just click the icon next to the address bar and any outstanding notification will be shown. You can mark them as read and then they disappear. There is a do not disturb mode where you won't be notified of anything.
Note 1: The extension says 'stackoverflow', but it shows all the notification from all the stackexchange sites.
Note 2: The Facebook private messages haven't been coming to me, some other person in the reviews said he had this problem as well (I don't know why).