You can register username/password combinations for a particular server and Basic Auth Realm (the text that appears in the IE password box). Like so:

my $mech = WWW::Mechanize->new( autocheck => 1 );

$mech->credentials( 'members.easynews.com:80', 'EasyNews',
    'username' => 'password' );
[download]

This way, WWW::Mechanize will figure out for itself when it needs to use the password, if your spidering takes you between authenticated and non-authenticated sections of a site, or between sites altogether.