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If you were invited to attend another person's webinar and are asked to enter a webinar password when join, then that means that the organizer who scheduled the session has password-protected the it for added security. This does not mean that you need to log in to a LogMeIn account; you just need to enter the password that the organizer set.
GoToWebinar does not store the passwords for password-protected webinars to ensure the security of your session, so the organizer should have provided it to you separately (most likely in the Invitation email). Please contact the organizer and ask them for the password if you can't find it in any prior communications.
Note: If the screen asking you for your password does not look like the ones shown below and also has a spot for "Email address", then you are actually being prompted to log in to an account. See Why am I being asked to log in? to learn more.