It’s interesting to see all of these design trends come, and then find new solutions and go; or trends to come and saturate, take up the market and become common place. Responsive Design may just be one of those fads. Like Ajax, the technologies have always been there, it just took a few clever minds to mix up the JavaScript and make the experience all that much more fantastic.
So what is Responsive Design? The ability to take a single website and allow it to be productively viewable on multiple different devices with various sizes. Adding JavaScript to snap the layouts into place and add flows makes Responsive Design very fun. But there are ways around Responsive design, and these include mobile and tablet based browsers. As mobile and tablet based browsers get more and more advanced, they learn to compensate for websites that are not design ready for multiple screens.
That said, take a look at some videos and learn a little bit for yourself.
I am not sure how much of a barrier websites without Responsive Design will become, but I would strongly agree that the implementation of Responsive Design implemented strategically for device sizes, in the addition of touch vs cursor input, greatly aid in the ease of use and functionality.