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.
Great post by Scott Switzer and wholeheartedly agree - an API is becoming genuinely essential to launching a online company - and for companies starting from scratch, the API should be first on the drawing board.