Login information for demonstration accounts should be permitted in questions.
% If you're asking questions about a site, letting people visit the
site is more effective than any number of words and screenshots.
% When asking a question, you want to do as much for potential
answerers as possible. Forcing them to create an account (often
requires giving out an email address, which some people dislike) and
then configure the account properly (not trivial in many cases) is a
lot more work for them than giving them to access to an
existing properly-configured account.
% The more work a question requires, the fewer answers it will
receive. Filling out a form, waiting for email confirmation, and
configuring an account just to start on the problem is a lot of
work, and certainly discourages people from casually browsing to see
if they can help.
It usually doesn't violate TOS:
% Many websites ask you to insure your account isn't accessed by
"unauthorized parties" or that "you are responsible for access to
your account". However, posting account information on stackexchange
sites means that you are authorizing stackexchange readers to access
your account and are accepting responsibility for their access to
% Generally, I can transfer any rights I have under a site's TOS to
others. Some sites' TOS forbid transferring access, but these are
generally sites that provide access to things of value such as
pictures, movies, songs, etc.
It's on-label use:
% Demonstration accounts often exist to help users understand how a
site works. Anything that helps the user understand how a site works
(or whether to sign up for a real account), including having
stackexchange users visit the site and offer their opinions, is a
legitimate use of a demonstration account.
% Since any stackexchange user could get a demonstration account
anyway, the site is in no way harmed if someone uses an existing
demonstration account. Providing access to an existing account is
simply a convenience and a shortcut, not a method of providing
Of course, the above doesn't apply to all sites. For example, a site
that provides demonstration accounts only to people meeting a certain
criteria may not want other people accessing the site.
However, the notes above apply to many sites, and a blanket ban would
be overkill and do more harm than good.