Donald -
I infer that you really mean the 'system tray' which normally resides in the right lower corner of the monitor. For Windows XP, you can customize this list:
Start Menu > Settings > Task Bar & Start Menu > Customize
However, you have already done this, and certain applets automatically reappear. So I have a couple of suggestions:
1) Double click the offending applet, and look for a checkbox that keeps an applet in the system tray. Remove the check.
2) Open the application that posts an applet in the system tray, and search all 'tools' and 'preferences' menus for an option to display (or not) an icon in the system tray.
Check your startup list to see if the offending application is loaded on booting. If you would rather it not load, you can remove it from the startup list. Look in the Programs > Startup folder, and if you find it there, delete the entry (the entry is a shortcut - deleting it does no violence to the application).
Alas, not all startup programs appear in the Programs > Startup folder. There is an excellent anti-spyware program (Spybot Search & Destroy) written and maintained by Patrick Kolla:
http://www.safer-networking.org/en/index.html
which does much more than prevent espionage. Under 'tools', you can open a 'startup' list. Uncheck anything you don't want automatically loaded at boot. This is safely reversible. Spybot Search & Destroy is 'beggarware' - these guys have earned a donation.
If your computer allows you direct access to the startup list (msconfig.exe), you can edit this list directly from graphic user interface (GUI). I'm not terribly keen on editing the registry for objectionable system tray icons, but if you know what you're doing, go for it.
Another way to determine what loads at startup is the Task Manager (Ctrl-Shft-Esc in Windows XP). To identify these processes, check:
http://www.processlibrary.com/
I recommend disabling one process at a time, and confirming that no violence has been done. It's a good idea to create a Restore point in System Restore if you're the type who gets impatient and wants to change a bunch of settings at once. That way, when disaster strikes, and you don't know which essential process you have killed, you can recover the computer to a working configuration.
Hope this helps.
Rick/Portland, OR