Here's a little action I wrote recently, to automatically populate a specific YouTube playlist as new videos are being posted to a Drupal site, using modules Trigger or Rules. The same concept can also be used retroactively on existing content, using Views Bulk Operations: select all existing video nodes and apply the action to them.
Actions are a convenient way to package functionality in reusable chunks that can be called upon specific events. Countless modules expose actions, and at least the following consume them:
I found it useful to manually call actions in the business logic as well, typically during form submissions or in hook_nodeapi.
One of the useful Web patterns I've been noticing has to do with item lists and bulk actions. Given a list of items, add a checkbox in front of each item, and let the user select an action to be executed on the checked selection. Specifically, I've seen it in phpMyAdmin, Mantis, and Google Mail.