bbPress.org

This turned out to be a clash with the admin-message plugin (wpmudev.org).
If I comment out the include_once statement at the very bottom of admin-message.php, which pulls in all the spammy advertising stuff WPMU put into your admin pages, the forum menus reappear.

As this issue seems to occur with quite a few plugins, it might be useful to draw up a list of plugins which cause compatibility issues with bbPress.

If you know of any please comment in this thread.