Imgur has an API. From the "Overview":
Imgur's API exposes the entire Imgur infrastructure via a standardized programmatic interface. Using Imgur's API, you can do just about anything you can do on imgur.com, while using your programming language of choice.
The Imgur API is a RESTful API based on HTTP requests and XML or JSON(P) responses. If you're familiar with the APIs of Twitter, Amazon's S3, del.icio.us, or a host of other web services, you'll feel right at home.
This version of the API, version 3, uses OAuth 2.0. This means that all requests will need to be encrypted and sent via SSL/TLS to https://. It also means that you need to register your application, even if you aren't allowing users to login.