Don Norman, design critic and usability expert, says "The new me is beauty..."
This is a shift we've seen among many usability experts. The idea is that usability should be priority #1. But usability alone is not enough. You should also strive to create a stronger emotional response with your product, and that doesn't mean compromising usability.
I know you cited graphic design in your question. And I think there are many cases to be found where good graphic design improves the effectiveness and popularity of a website. Heck, I've seen a 50% increase in returning visitors after making my homepage a little more fun and engaging. But I'm going to talk about an even more controversial subject: animation.
An example of these principles at work is the new Windows Phone 7. The UI is fluid, natural and easy to use. "Clicking" a button causes it to shrink momentarily, making it obvious that you've actually clicked it. This animation plays out in a fraction of a second before the next screen would have loaded anyway. Little details like this improve the perceived responsiveness of the UI.
Are animations necessary to make a good UI? No. But this is a case where the animations and motion tweens provide instant feedback to actually create a more pleasant user experience.