In Tools | Customize…, in the Shortcut page, uncheck Display a tray icon when Windows Starts and Display a tray icon when EmEditor Launches.

Alternatively, you can set this in the installer. When you run the installer, make sure the Add the tray icon on the task bar check box is unchecked during the setup. You do not need to uninstall EmEditor before running the installation again. If this does not work, select Search from the Windows Start menu, and search for “emeditor.lnk”. This file should be located in the Startup folder. Delete this file to remove the tray icon permanently.