My goal is to write integrate a forum software with my shopping cart software.
For example, my application will automatically register the shopping cart members as forum members.
What forum software has a good API or extension capabilities that will allow me to do this?
Does it have to be an api?,
i did similar using phpbb but just wrote directly to the database, most have db layouts that are easy enough to work out ?
Vanilla is a well designed piece of forum software for PHP, extensibility is a first-class citizen of the design process.
Of course, all major players in the field will offer some way to integrate with their forum. With enough time and effort, it would be possible to create some form of integration layer and support multiple forums, providing your users with a choice. Not a task I would envy you for, mind you.