I am of the belief that in contemporary media sound is just as important, if not more important than it used to be, as well as equally important as the visual.
You can have the most impressive, most advanced graphics in the world (take Avatar, or Transformers), but without sound that is equally as impressive a feat, you can't sell the graphics, and the viewer is taken out of the experience.
The more that big pictures up the ante with visual effects, the more sound has to step up to match it. Think back to when Star Wars came out. It was incredible. Nobody had ever seen anything like it before. Nobody had really been a sound designer before either. If they had just put every day sounds to Star Wars, the audience wouldn't have believed it. What Ben Burtt did was create sounds than nobody had ever heard before to go with the picture that nobody had ever heard before. That was the only way to make it remotely believable. And what a fantastic job he did!
Now that anywhere from 30% to 100% of the picture is CG in most blockbusters, sound is the "Glue" that holds the picture together. A giant CG robot can only look so lifelike. It can't be perfect. What takes your mind off of the imperfections is the organic sound it makes.
Stepping away from movies from a minute and touching on mobile and internet media, I think sound is just as important. Sound has become a sort of tactile feedback. You roll over something on the internet or press a button on a device and it makes a sound, however subtle it might be. You take that away, and it completely changes the experience. Sound is immersive, it's what completes an otherwise incomplete media experience.
My 2 cents