How to Edit the Notification Area of Taskbar
This will open a window that will give you access to a host of options. Of particular note are the two links at the top. First, click Select which icons appear on the taskbar. Here you can turn specific program icons on or off. Turning them off will relegate them to the icon area that opens when you click the upwards arrow on the notification area.
Now go back and select Turn system icons on or off. This time, turning the icons off will remove them completely. Of course, the functions themselves do still exist on the system and are accessible through other routes, they just won’t be on the taskbar.