Background: had a working Wordpress 3.7 site at olddomain.com.
I moved it to newdomain.com successfully, and in the process added this to wp-config:
I experienced this due to my caching plugin.
W3 Total Cache had added the following to my wp-config.php file:
define('COOKIE_DOMAIN', 'www.olddomain.com'); // Added by W3 Total Cache
Since it was hard coded, it didn't update to the new site domain. After deleting the added code (because I don't currently use the plugin), I was able to log in again.
I'd check wp-config.php for the word "cookie" to see if a plugin might have added something like this.