We have deployed a new feature that hopefully help with keeping you instantly updated as new questions and answers are posted. All sites except for Stack Overflow have a new activity indicator on the homepage which will show when new posts are asked or answered.
We have also enabled updates on the questions page for the newest and active tabs for all sites except Stack Overflow. If you open a browser to these tabs you will receive instant notifications when new questions are asked or answered.
Stack Overflow has a massive amount of activity so we have decided to limit this feature to tags only. Both the "newest" and "active" tab will have updates after first selecting a tag or tag combination.
We recently added support for new answers and comments:
Now for the gotchas - in order to use this feature you must have a browser that supports web sockets. See: http://caniuse.com/#search=websockets for a list of browsers that currently support web sockets.
UPDATE As a few have mentioned below we are now experimenting with updating comment counts, votes on a post, and your reputation score.