Should threads have special design to be shutdown gracefully by Tomcat?

... and to tie the other responses to the workings of Java Servlet environments;

if you don't declare your threads as daemon threads, the way to signal the server shutdown to the threads is to implement a ServletContextListener and configure it to your web application (web.xml). When Tomcat is shutting down, it will first shut down each application, which in turn will cause contextDestroyed() method of the listener to be called - and this is where you can signal your own threads that they should finish their work.

Any threads that are still running will keep the Java (Tomcat) process alive. Make sure all your threads exit. Once your threads exit, Tomcat will be able to shut down.

See the javadoc for Thread. Note the following:

The Java Virtual Machine continues to execute threads until either of the following occurs:

• The exit method of class Runtime has been called and the security manager has permitted the exit operation to take place.
• All threads that are not daemon threads have died, either by returning from the call to the run method or by throwing an exception that propagates beyond the run method.

You need to cancel your threads, preferably by calling interrupt on them and making sure they are written in such a way that they respond to the interruption -- meaning, checking their interrupted flag and responding intelligently to InterruptedExceptions (not just eating them and continuing on).

The above advice assumes you don't want your threads to drop what they're doing immediately. If you are ok with that then make them daemons.