Rand Fay (aka rfay) talks about the Examples for Developers module, which creates functioning examples of a lot of the core Drupal 6 and Drupal 7 APIs. There's also a demo site for Drupal 6 as well as a Drupal 7 demo site where you can see the examples in action. These examples are also include within api.drupal.org, and you can browse all of them by searching for "_example" for Drupal 6 as well as for Drupal 7.