I've noticed that MediaWiki websites such as Wikipedia display a "you have new messages" message whenever a change is made to the user's talk page. Is it possible to get the same type of notification for pages on the user's watchlist?
This is soon going to be possible when the new Echo extension gets deployed to the English Wikipedia somewhere in March 2013. There will be a unified notification system for changes in your watchlist and your user talk pages.
Note that in a vanilla install of MediaWiki, such a feature does not exist.