Is there a notification api module? I like to have a general api for sending notification. I am not sure if there is out there somewhere for Drupal.

For instance, is should be possible to provide a node id and some criterias for which users to send notifications to. The options could be something like "not to the node author", "all who has commented on the node except specific ones (perhaps a comments that has just been written), true/false on sending notification to user who already got a notification about new comments, etc.

There are probably other notification scenarios that could be supported. It would be nice with a general notification framework for Drupal. It seems to be lacking right now (I have looked at subscription and notification). However, I am new to Drupal and might have missed something.
There is a Notifications module for Drupal that creates a framework for sending out notifications. There are already many modules using the framework. There's a development version of an extension module called Notifications Rules for integrating this with the Rules module if needed.