The API module implements a subset of the Doxygen documentation generator specification, with some Drupal-specific additions. Standards for how to write Drupal documentation that this module can parse (and that conforms to Drupal coding standards) are on http://drupal.org/node/1354.
Note that whatever version of the API module you are running, you can set up an API site to display code/documentation from any Drupal version, so in some sense, the version of Drupal you are running your API site on doesn't matter too much.
The API module has now been ported to Drupal 7. It is recommended to use the latest stable 7.x-1.x release.
Note: If you upgrade to 7.x-1.7 or a later release, definitely read the release notes for version 7.x-1.7 for important notes on Grammar Parser and PHP versions.
Note 2: If you decide to use a -dev version of the 7.x-1.x module, read the release notes as there may be other patches that you need to install.
Version 6.x-1.9 will be the last Drupal 6 version of the API module, and it is no longer supported. Use the 7.x version instead.
This project is under the active maintainership of drumm and jhodgdon. We welcome your contributions via the issue queue (see sidebar). The issues in the issue queue are regularly updated so that our highest-priority bugs and feature requests are marked with status "major" or "critical", so start your searching there to have the biggest impact.