The area you are referring to, is called the system tray. These are programs loaded at startup, which basically sit idle, waiting to be called upon. The reason for their existance, is for faster program start up. For example, scanning software, CD-RW software, audio adjustment sofware, and most importantly, virus scanning software icons all reside there.
There are several methods that can be employed. First, try single right clicking on the offending icon, and enter properties. Some will let you select it not to run at startup. Many don't have this feature here.
Next, try Start>Programs>StartUp, and check if any are here. Some will, others still won't.
Like Beth said, you may have to uninstall the software, and reinstall it as custom, and look for the option to not run at start time.
As a last resort, the registry can carefully be edited, to remove references in there.
Run regedit, and follow this path: H_Key_Local_Machine>Software>Nicrosoft>Windows>CurrentVersion>Run
All the software loaded to the system tray is executed from this very registry key. You can delete the key referring to the software you no longer want to run at startup.
YOU MUST BE VERY CAREFUL IN THIS AREA!!! It is perfectly ok to browse around a little, just pay close attention before you delete anything. Only do this if you are comfortable with the potential risks involved.
And yes Regis, it is my final answer.