There is not currently an API offered by Google Latitude.
Does anyone know of plans for being offered in the future?
If it does, what social networking applications for this technology can you think of?
I don't know of any plans yet, but I'd be extremely surprised if Google doesn't intend to take Latitude in a direction similar to the OAuth-enabled API provided by Yahoo's Fire Eagle.
There are already dozens of good applications built on Fire Eagle that will likely be duplicated on Latitude. Ideally, Latitude and Fire Eagle could agree to speak the same protocol, at least for the most common tasks such as updates and location queries--this way, client applications could be written to work with either one or both, and users could choose where they'd like to store their location data.