How much data do Facebook applications have access to?

Question

When I allow an application to access my data, what information can it actually access?

Answer 1

It used to be that applications had full access to all your data, but now it's more restricted:

instead of granting access to all of their profile data when engaging with an application for the first time, users will now authorize only specific categories of user data – like interests, gender, or their current city, for example. With the changes, when developers want to access new profile information fields not granted in the original application authorization, they’ll need to ask for explicit permission.

Source

So the application should ask you for permission and tell you which categories of data it wants access to. So if you're not happy about letting an application having access to your photos, for example, you should be able to tell and not install it.

Answer 2

The new permissions model is now live, giving you, the use, more detail into what exactly is made available to the application.

Source

With this new authorization process, when you log into an application with your Facebook account, the application will only be able to access the public parts of your profile by default. To access the private parts of your profile, the application has to explicitly ask for your permission.