Who ever said that institutions were loathe to change? Well call him up and let him know, the Library of Congress, with their Prints and Photographs API has finally taken the REST API plunge. If this government institution can do it, maybe you can convince the head of your IT department that APIs are a good idea too.
I love the way that the Prints and Photographs Online Catalog has done it. Every page on the site can be instantly serialized in json with a simple modifcation of the URL. Simply adding "?fo=json" to indicate the JSON format turns a page displaying an olde tyme tap dancing class into JSON data.
The Prints and Photographs API documentation is clear and straight forward. Search functions are exposed through the API. The parameter list available as search options is decent, allowing for keyword and collection based queries. More refined search filtering could be achieved by drilling down into the meta data on each individual item returned by the search. Maybe the Library of Congress is looking for a great iPhone search app? Will you be the one to create it?