- It looks like in some situations, Facebook will send an email that has a link. That link expires after a certain amount of time, but in the mean time, clicking that link lets people access that Facebook account.
- A large number of services can be set up to automatically post any email received onto the web. One major category is disposable email services such as asdasd.ru. Any email to a throwaway account on asdasd.ru gets put up on the web. Here's an example Facebook recovery email that got turned into a web page: http://asdasd.ru/read/414831
- Once these emails are just webpages, it's no surprise that search engines discover those URLs. Note that this is not a Google-specific issue. When I search on Bing for the query [site:facebook.com bcode n_m mid], the first result is also one of these urls that has an email address embedded in it. For a debunk of the misconception that this is related to the Google Toolbar or Chrome, see my post elsewhere in this discussion at http://news.ycombinator.com/item?id=4733276
So: an email gets sent to someone. That email gets put up on the web as a webpage. Search engines (including both Google and Bing) find that webpage as they follow links on the web.