For the answer, you need look no further than Yasujirō Ozu. The creator of what are now thought of as the most Japanese of all films from the late twenties to the early sixties, Ozu mastered many elements of cinema. Most of all, he mastered the pillow shot. This is so much the case that to define the pillow shot is simply to describe Ozu's use of pillow shots. Usually capturing some element of the natural or architectural environment — or, best-case scenario, both at once — pillow shots appear in a narrative film while having nothing at all to do with the narrative itself. Their purpose is entirely rhythmic and aesthetic.
An adept use of pillow shots indicates, to my mind, that a filmmaker's priorities are in order. That is to say, they're not out of order. It's easy to see a director dismissing the very concept of pillow shots because "everything in a movie should move the plot forward," but isn't that like insisting that everything in a movie should, say, advance its aesthetics? Or that everything should be subordinate to the rhythm? I'm pretty damned suspicious about assertions that every element of a film should serve the same end, especially if that end is jerking characters around.
I've thus started making use of pillow shots in my own movies. In fact, I can't imagine not doing that. And for pillow-y ideas, there's no finer place to go than the Ozu-devoted ozu-san.com, which maintains a pillow shot screen capture archive. Some of my very favorites follow. I just want to get high-res versions of these, print them, frame them, and hang them around me as an undrying fount of cinematic inspiration.