As is already mentioned, the "ScriptListener" records every step you take to the "ScriptingListenerJS.log" and "ScriptingListenerVB.log" files on your Desktop.
The only way to stop recording is to delete the "ScriptListener" file in the "Plug-ins/Automate" folder (under Mac OS X, you may also need to empty the Trash).
However, if you happen to record scripts every now and then, you don't need to uninstall the plug-in. On the other hand, if you never remove the log-files from your Desktop they can grow too large.
Perhaps, the most sensible solution is to automate the log removal as follows:
1. In the main menu, choose "File > Scripts > Script Events Manager".
2. Check the "Enable Events To Run Scripts" checkbox.
3. In the "Photoshop Event" menu, choose the "Start Application" item.
4. Make sure that the "Script" (and not "Action") option is selected. In the "Script" menu, choose the "Browse" item, browse to ".../Script Arsenal/Scripts/Scripting" and choose the "Delete Logs.jsx" file.
5. Click "Add" button (screenshot).
From now on, the log files will be automatically deleted every time you start Photoshop.