Fred Wilson wrote a post about how companies build their mobile presence first, and their web presence second, showing a shift in how people use the internet.
I would probably modify this idea, with the following:
API First, Mobile Second, Web Third
The most important consumer of your product in this age is not necessarily a person, but a machine. By building your API first, a mobile presence and/or a web presence can be built on top for your users. In addition, other companies can use your site to add value to their own - your product leverages the network effect before either a mobile or web presence is built.