How do you verify your YouTube account?

If it is not a problem for you to browse YouTube as anonymous user (non-logged-in), then you can get rid of that annoying prompt for entering your passWord.

If it asks you for a passWord, then you have been logged-in in past and the information about your last used account is in the cookies. So close all the Windows with YouTube pages, delete the cookies for domain YouTube.com (or all the cookies if you don't know how to delete just specific ones) and then go to YT and it will not require a passWord anymore.