Are you e-mailing your users to tell them about a new feature? Why not show them an in-app message instead, when they are logged on and engaged? Are you e-mailing a custom offer to a certain segment of your user base? Show them the offer when they're on your site.
Obviously, if you are contacting users that are not visiting your site at all, then e-mail is still king.
Personally, I am glad to see Gmail implement this kind of separation so well.
Full disclosure/plug: I work for Evergage (http://evergage.com) and we provide this behavioral-driven in-app messaging.