Why can I not login on my live site?
Please check:


your cookie_domain value in your settings file

Normally it should work when it's empty, however if you're using across multiple domains or protocols (e.g. form is HTTP, but you're submitting to HTTPS), you should set it to its full domain name, so Drupal automatically generates a unique session cookie name for each site. E.g.

$cookie_domain = '.www.example.com';


or assign it dynamically like (not recommended):

$cookie_domain = @$_SERVER["SERVER_NAME"];

watchdog logs, e.g. drush ws --tail,
if you're using LoginToboggan or similar, check whether you should use username or e-mail to login,
whether cookies are created fine in DevTools console,
if you're using Varnish, check whether cookies are deleted,
try login to the site using one time login link, e.g. via drush uli command and verify that your account works (it's not blocked or something),
try in another browser or in incognito mode,
disable any 3rd party authentication modules (ldap, openam, etc) which may override the default logic,
debug your code using XDebug.