Sidebar content always gives me a little twinge when it comes to responsive design. Typically a left sidebar will end up stacking directly above the content and a right sidebar directly below. This can be fine, unless your left sidebar has 5 different content areas and now the user has to scroll two screen lengths just to read an article. Or the right sidebar has an important call-to-action you apparent to each visitor, but it resides underneath the content on a mobile device. By using separate regions and floats a single sidebar can easily be broken into two creating a responsive sidebar and giving you more room to play with responsive design.
Take for example a structured template like so
A responsive sidebar utilizes breakpoints to give you greater control over your design. This causes the section.sidebar-bottom to float underneath section.sidebar-top and keep the content area to the right of the sidebar. In this case we just set up a left sidebar that has a breakpoint we can utilize in responsive design.
For my website I set a breakpoint for tablets - keep the top of the sidebar aligned left to the content, but stack the second half of the sidebar below the content.