You need a mobile website. A few years ago you didn’t necessarily have to have one, but times have changed. More and more people are accessing websites on their smartphones, i-whatevers and tablets. Your site needs to be ready.
With responsive design your website will respond to the device it is viewed on. If it’s a small device, columns will stack, navigation will be handled differently, images will shrink. All your content will be available to anyone, anywhere.
A mobile-specific site can look very different than your desktop site. In some cases it may have more of an “app” look to it, it may not show as much content or may show all the same content.
Responsive or Mobile Specific?
It’s really up to you. It can be a matter of preference (maybe you really like the app look that can be achieved on a mobile specific site or maybe you prefer the one-size fits all).
Mobile-specific sites often have their own domain which means your website statistics may not be as easy to keep up with. With responsive design statistics are cataloged exactly the same whether your site is accessed on a smartphone or a desktop.
Responsive is my preference and recently Google announced it as their preference too.