Google Recommends
Responsive Design for Smartphone-Optimized Sites

Smartphone and Mobile devices

Dec,08/2014: Internet Explorer is implementing srcset with x descriptors
Jul,22/2014: The "picture" element is finally, officially, definitely going to ship un-flagged in Chrome 38 and Opera 25. Canary builds from here on out will support the feature by default, too. Much implementation work remains to be done. picture, srcset, and sizes have been fully implemented in Gecko but are still behind flags in Firefox Nightly. The WebKit implementation has a ways to go. We're still waiting on an official "yes, we're implementing this" from IE. And it will take a while for these features to trickle down to mobile browsers, where they're needed most. But! It feels great to have one foot, firmly planted. Andreas Bovens posted something great.
Feb,26/2013: W3C Working Draft Published
Dec,11/2012: I have agreed to the W3C Community Final Specification Agreement (FSA)

Google officially announced this recomendation at June,6/2012.

You wish to know more about "what is" Responsive Web Design? Here it is by "Ethan Marcotte".

"Responsive Web Design" (RWD) is being discussed since 2010. "Filament Group" wrote at Dec/2010: "Responsive Web Design has been a very hot topic this year, inspiring developers who long for a "one codebase serves all" future. But critics of the technique have pointed out several issues that need to be addressed before it can scale perfectly from handheld to desktop — specifically, while HTML, CSS and JavaScript can be light enough to share across all experiences, desktop-optimized images are often too heavy for mobile connections, and mobile-optimized images are too low quality for desktop viewers."

W3C created at Feb/2012 a "Responsive Images Community Group" (at Jul/2014 with 366 participants - I am one of them). You can find the Proposal here.

At Nov/2011 "Katrien De Graeve" wrote: "Responsive Web design is in its early stages. Web designers will continue to offer different opinions and recommend directions related to whether to build for mobile first, how to fit these decisions into the design process, whether to slice up the comps into all the different screen sizes, and so forth. And as more and more screen sizes and form factors arrive, the conversation will continue.
HTML and CSS standards are evolving to help Web designers deal with these issues. It’s clear that some form of responsive Web design will be used to meet the challenges, and it’s equally clear that standards will continue to evolve as better ways of handling the changing world of devices and browsers are discovered.

OK... then we see a lot of people coming with "solutions" - Google for it and you will find dozens. Here is a Website with free templates (looks like to be very good).

BUT... Does it worth? Maybe not: 5 reasons why responsive design is not worth it.

Maybe some people are missing the point?

Every Website should use responsive design?

In my opinion Google made an irresponsible(!!!) recommendation. There is still a lot to talk about and maybe a solution to replace images (for example) will not come up so soon. FOR NOW... I recommend Open-Realty® Website owners to NOT go with "Responsive Templates"!

I strongly agree with "Brad Frost" words: "Your visitors don’t give a shit if your site is responsive. They don’t care if it’s a separate mobile site. They don’t care if it’s just a plain ol’ desktop site. They do give a shit if they can’t get done what they need to get done. They do give a shit when your site takes 20 seconds to load. They do care when interactions are awkward and broken."

Finally, according "Morgan Stanley" we don't have too much time to find a solution:

Mobile Users versus Desktop Internet Users

I recommend you to read:
May,07/2012: Responsive image format by Yoav Weiss
Dec,11/2012: What We Thought We Needed by Paul Robert Lloyd
Jun,25/2013: This page captures relevant blog posts, email threads, etc

Eduardo Marques (a.k.a. "ebmarques")