I think one of the best ideas behind a one-page site is that there's more of a narrative aspect to it. The best example I can think of is this page: An engagement/wedding invitation site. This is an incredible site, and it works for a lot of reasons, one being that everything flows so nicely together. It wouldn't have the same impact spread out over a set of pages.
This demo that was originally made to show off IE9 is all about storytelling. Almost like a picture book, but with scrolling instead of turning pages. And because of that it's really seamless and cool. Not really practical for making a business site, but it highlights one reason why the one-page vibe is useful.
It also works with smaller pages with not a lot of content. When I got married I had all of our info on a one page site because there just wasn't enough content to warrant going from page to page. It was easier to build and maintain a one page site, and load time was not really a concern.
When it comes to business, I think it's a tougher case. I thought a memorable example was when Google launched its Nexus phone - they did it on a one page site. Since they've launched their tablet and announced their Q it's not like that anymore so I can't link, but it was really neat to see everything in one place. You reduce clicks and create a more immersive experience.
I think you'll be seeing plenty examples of people doing it just to flex their coding muscle or to try to capitalize on a trend. But that happens all the time in the design world. Keep it on the table when you consider your site's purpose and use it when appropriate!