With Responsive Web Design, you can make your website compatible with every mobile device and web browser that's out there using simple techniques.The number of mobile devices and web browsers have exploded in recent years and it is nearly impossible for any web designer to create websites for every device that is out there.
Responsive Web Design is a technique where you create a single design and it adapts itself based on the screen resolution of the client’s device which could be an iPhone, an iPad, a Kindle or even an upcoming Windows 8 tablet.
Responsive Design may be good for SEO as well because you aren't serving content over multiple URLs (the mobile page will have the same URL as your desktop page) and hence all the Google juice is preserved. Here are some excellent slides to help you get started.