Does anyone have suggestions for a PHP, Python, or J2EE-based web forum that has a good API for programmatically creating users and forum topics?

phpBB would be the first that comes to mind as open-source, simply because it's free.

In reality almost all forum platforms have some sort of 'api' in that you can do whatever you need programatically, it just may not be as simple as 'add_user(bob)'. A few lines of code and a SQL query or two and you can usually achieve everything you need.

Out of personal preference I would recommend vBulletin, however it does have a fee. The benefit of this is that it has a very strong modding community that have probably already accomplished everything you need at http://vbulletin.org.