I'm not really a rah-rah API guy from the perspective of governance, but they genuinely solve business problems, often in areas not directly anticipated by the API.
For example, suppose you're making a local website for Ogaki restaurants. Getting the addresses and phone numbers of all of them (a couple thousand) would be sort of difficult. Happily, their owners will be thrown in jail if they don't leave that information with the Ogaki food inspector, so if they have an API for food inspection results you can query it, toss the irrelevant data ("In compliance: No rat tails in soup", etc), and get your site bootstrapped in an afternoon.
but you haven't considered the cost of making such information available. Are you willing to pay some extra tax dollars to make such information available (even if you most likely won't be making use of it)?
This is pretty great -- question to HN: as a person learning how to program who has a somewhat tenuous grasp on python (i.e., I have done Project Euler up to 15, but I am daunted by full scale apps), how do I make the transition from learning the syntax to learning the methods of something like this? I feel tutorials can only go so far, but those are the only things I can think of to use to learn.
One approach would be to find a popular Python web framework and then follow the tutorials for that. Because you already have some familiarity with the language, the syntax won't distract you from absorbing the application architecture concepts.
I did that with Django -- I feel on the cusp of getting it, but the tutorial ends kind of abruptly. I'm working on a project to get my feet we, though (a simple tiered to-do that I am planning on integrating with a little under-construction site to show true %-done of aspects of a site).
Just try to write a programme? Make it work (well enough) first. then try to make it neater. Do you know any python programmers? Ask them to look at your code, they might asuggest things you didn't know you could do.
For example, suppose you're making a local website for Ogaki restaurants. Getting the addresses and phone numbers of all of them (a couple thousand) would be sort of difficult. Happily, their owners will be thrown in jail if they don't leave that information with the Ogaki food inspector, so if they have an API for food inspection results you can query it, toss the irrelevant data ("In compliance: No rat tails in soup", etc), and get your site bootstrapped in an afternoon.