<p>I need to signal a running application (Windows service) when certain things happen in SQL Server (2005). Is there a possibility to send a message from a trigger to an external application on the same system?</p>

You can send an email from a trigger, but it isn't a recommended practice becasue if the email ssystem is down, no data changes can be made to the table.
Personally if you can live with less than realtime, I would information about the event you are interested in to another table (so the real change of data can go smoothly even if email is down for some reason.) Then I would have a job that checks that table every 5-10 minutes for any new entries and emails those out.