Execution of a Java program by a trigger.

Yes, using the MySQL User-Defined Function (see MySQL 5.5 FAQ: Triggers) and installing the lib_mysqludf_sys

Then, for example, you can write your own trigger calling the sys_exec like this:

delimiter |
 CREATE TRIGGER testtrigger BEFORE UPDATE ON T1
  FOR EACH ROW BEGIN
   DECLARE result int(10);
   IF NEW.Flag <> OLD.Flag THEN  
     SET result = sys_exec('/path/to/javabin -jar your.jar');
     -- other kind of works and checks...
   END IF;
 END;
|

The result contains the exit code of the external program

There are other useful functions in this library:

• sys_eval : executes an arbitrary command, and returns it's output.
• sys_get : gets the value of an environment variable
• sys_set : create an environment variable, or update the value of an existing environment variable
• sys_exec : executes an arbitrary command, and returns it's exit code

More info here

Try it on a dev env and...

Be very careful in deciding whether you need this function. UDFs are available to all database users - you cannot grant EXECUTE privileges for them. As the commandstring passed to sys_exec can do pretty much everything, exposing the function poses a very real security hazard.

But anyway, I agree with the proposal of Remus Rusanu

I know this post is fairly old and sorry for picking it up but I recently had the same requirement, so I created a MySQL UDF that uses JNI to call Java code from within a MySQL trigger. I'm posting this as a reference for similar future requests. I've checked in the code in bitbucket. You can download it from here:
MySQLUDFJavaLauncher and here is also a link to the Instructions.
Maybe this will help others.