Intersect is a Google Chrome extension that lets you see users who mutually follow you and another user on Twitter. The API uses a RESTful interface and responses are formatted in JSON. The simple API is documented on a GitHub repository and it is open source (MIT license), so you could run your own version of the service.
So and So is now following you on Twitter. Who? How did they find me? Why might I want to follow back? That's been a common bit of internal dialogue for me lately. Often the answer lies in our mutual friends or followers. Social networks like LinkedIn and Facebook make this easy. Not so with Twitter, which is why I was excited to find Intersect.