Facebook does have an API, but unfortunately, you cannot use it without acquiring a secret key. Because Facebook gives users control over their data privacy settings, there is no "public access" to data retrieval methods. You must have a key in order to start fetching things.
All facebook applications are given a secret key when they are created. Users can prevent applications from retrieving their data if they want, hence the need for an associated key.
Facebook Connect applications function in the same way... they are assigned a key that is used remotely from a third-party site (ie. yours).
Unfortunately, without one of those keys you won't be able to access any data, even your own. You could probably come up with a work-around by making your own application and using that key to fetch data on yourself, but you'll need to go through some hoops to make it work on a permanent basis (ie. without a new session each time), like granting the offline_access
extended permission.