Luke points to the sweet spot between creating endpoints for classes of devices, and using responsive design to allow them to adapt.
A concise case study from gov.uk:
Designing for the constraints of mobile is useful – if we get the fundamentals of the service working on small screens and slow network speeds, it can work on more capable devices.
Yes! Yes! Yes! Mark nails it: just because someone visits a site with a certain kind of device doesn’t mean you can make assumptions about their intentions.
An excellent article from Bryan, hammering home the point that there is no sharp dividing line between desktop and mobile.
Remember as well that the most ubiquitous of technologies, the common thread throughout many connected devices, is the browser. Browser-based experiences may not always be as sexy, but they are often far more capable of adapting to different contexts. In times of rapid change, adaptability—rather than features—may be your product’s greatest ally.
An excellent overview of the evolution of the St. Paul's School website from David Smith, noting an increasing emphasis on mobile usage.