I don't think that standard java  supports this. However, I do believe
that the SWT graphics package from IBM (for java) does.

This is possible in Tiger, see an article on sys tray on sun. If I am not
wrong then there was a complete tech tip in last month sun technology
letter. They have introduced a complete api to support windows desktop
facility including, IE, Sys Tray and many more.

Im not able to find any link about SysTray
enhancements in Tiger... But i hv find some JNI
methods to put  SysTray icon  using java  on this
following URL...

http://jeans.studentenweb.org/java/trayicon/

Ok I have spent some time to explore my browser history, here are exact
links that I told you,
The following link has the demo , hit for a JWS demo run , satisfy yourself
and then write for you with org.jdesktop.jdic
https://jdic.dev.java.net/

This is the image showing exactly what you want.

https://jdic.dev.java.net/resource/trayicon.gif

regarding your problem  on having a Java
Application running on system  tray instead taks bar.
I don't know whether that is possible using Java or not, but I have a method
which might be of some use to you. Whenever you create  a JWindow, according to
my knowledge, no task bar button  is generated, so you just make a JWindow and
just make it transparent and use it as an application.
And in that give an option for the user  to use small mode, which runs just above
the system tray. Hope you understood this method.