How to Prevent a Windows 95, Windows 98, or Windows Me Logon Prompt at Startup
*Note: If you have user profiles this will not work as stated in the article and you will have to perform the steps in the link provided in the article for user profiles.
It has also been advised that you do not use the article Q135586, which has a link included in the article. Its purpose is "to clear the User Name logon box so it is blank each time you start Windows", it is not meant to prevent the logon box from prompting you for a name/password.
Instead if you have TweakUI installed, check to make sure the "Clear Last User At Logon" check box is not checked. Go to Start > Settings > Control Panel, double click Tweak UI, click the Paranoia tab, if the box is checked, uncheck it.