As this API has just launched, it is highly advisable that you let me know if you build an application so I can contact you should any of the API details change - it's also great to see what people are building and take your feedback on board to improve the service! Alternatively, you can subscribe to the web log on my website or follow @WikiLocation on Twitter for all of the latest updates.
I'm an iPhone / iPad Developer and whilst working on one of my pet projects, Gowalla Tools, I was interested in displaying Wikipedia entries by location. I had assumed this was a fairly trivial task as I had seen a couple of other websites and iPhone apps with similar functionality. I thought that this would be something provided by a Wikipedia API but was surprised to find that this was not the case. After a lot of searching, I found a site that offered Geo-coded Wikipedia entries via an API but it was using very outdated data and the API was fairly slow to respond. Further investigation confirmed that all of the "Nearby Wikipedia Article" apps I'd seen were using this data (or similarly small datasets).
As the developer of the popular Tube Updates API, it became apparent that if I wanted to search Wikipedia data by geo-location then I'd need to do it myself (and I may as well open it up as a public API). The result is WikiLocation - a RESTful API for all of the geo-coded data on Wikipedia consisting of almost 1 million records from the English version of Wikipedia alone!
As well as being able to search by Latitude and Longitude, you can also search by FourSquare or Gowalla spot IDs making mashups between these services trivial.
To start using the API, take a look at the documentation.