Responsive Web design, despite its buzz worthy status in the design world, is not the right fit for every website. Know the risks, and rewards of this critical design principal before investing in such a tactic.
Banking vs Email
Two good examples of the kinds of things people often do with a mobile device are check emails and bank accounts. Of course, this also entails drafting emails and conducting banking transactions, but the kind of website in question is almost as important what people actually do with it.
For mobile banking, many customers are there to do a quite small number of things, and so many banks don't use a responsive design approach at all. They simply build a more compact mobile version of their websites for people to check balances and maybe transfer some funds.
Doing so means adding a separate URL for those mobile sites, and that does add complexity, but some of those banks likely see that as just the cost of doing mobile business. It's a common practice still, but with the rise of responsive design, more and more companies will no doubt be looking at what it would take to phase out their mobile sites in favor of a build once, responsive approach.
Online banking is popular enough, but way more people are checking emails via mobile devices, and companies like MailChimp and Yesmail have indeed adopted responsive designs. Anyone viewing messages in either of those systems would be viewing the same content as someone on a laptop or desktop, with just a few minor adjustments for doing so on different sized screens.
Nearly 60% of American adults now own smartphones, so there's no doubt the idea of operating and maintaining separate websites for mobile and desktop visitors will increasingly come under scrutiny.
Retrofitting Often Not an Option
Beyond the approach of dedicating mobile sites to those tablet and smartphone users, there is also dynamic serving of Web content. This is not quite responsive design, though this technique does involve telling a webpage that it is being viewed on either desktop or mobile devices. The rest of the magic is done using CSS, so this technique will likely be a popular way for companies to begin moving toward responsive designs.