Here are some sites that I have developed using responsive web design. As you make the browser window smaller - or view the site on an iPad or and iPhone, the layout changes to work with the size of the screen.

Two of these sites are using Yoo Theme Nano - which has a great deal of responsive design built in.  This being said, if you rework the styling to the extent that we have for these sites, you still will need to make some special styling for the iPad and iPhone layouts.  The Yoo Themes/Warp 6 create mobile menus by converting the menu into a select pull-down list.  If you move the screen down on a standard monitor to the mobile device width, the menu is simply a pull down menu, but on an iPhone mobile device, the pull down menu becomes a scrolling device.

The Freedom Mountain Investment site is using the basic beez_20 theme - modified quite a bit - so all of the responsive had to be done by me.  It does not have an extensive menu system like the others so that simplifies the process quite a bit.  The elements do rearrange themselves as the browser window narrows.