Responsive Web Design shows the user different elements -- or elements arranged in different ways -- by using media queries (if the device is a desktop or laptop, show them this; if a tablet, show them that; if a "phone," show them the other thing) or other methodologies.
What about, though (especially if your app/site uses MVC anyway), leveraging MVC to return different Views based on the type of device / user agent?
Each Model/Controller pair could have at least three Views (desklaptop, tablet, phone, as well as perhaps more granular gradations and/or Views tailored to larger devices) and, based on the size of the user agent's real estate, invoke the appropriate View.
I'm thinking this might be a more natural and easier to implement way of optimizing the experience for all users, at least for those conversant with MVC. How exactly this is implemented (how the user agent is determined and the appropriate Controller ActionResult is invoked) I'm not sure, though... thoughts?
Response to the comment and answer:
I'm thinking more along the lines of this scenario, for which, IMO, media-queries won't satisfactorily handle:
Your app/site has as its centerpiece a map. There are ancillary but vital pieces that are placed around the map (top, botton, and side) that all fit on a tablet (barely) and larger devices just fine. On a phone, though - no way - there's only room for the map, and even then the map is almost too puny.
The only way I can think of to deal with this is to show the map full-screen on the phone, with buttons or links in states like Wyoming, Montana, and Nevada that will invoke the parts that surround the map on larger devices but will monopolize the screen on a phone. In each case, the currently displaying View will need links to [re]open the other portions of the app/site.
Otherwise, the only way it could be usable with a phone is if the user is carrying a magnifying glass around with him (or zooming and swiping around the screen like a madman, but IMO that's a pain in the gluteus maximus).
And so, in such a scenario it seems to me that Views would be easier to implement than altering the CSS, as this is a major renovation of the screen, not just a rearranging of furniture.