At some point in time, I constantly had problems logging in to my WordPress Dashboard on one of my machines, using Firefox.
When I entered my user name and password, I’d always be redirected back to the login page, with no error message or anything. This only happened on one machine, and only in Firefox. Safari, Chrome, IE, they all didn’t show that effect. FF on other machines also worked like a charm.
Over at the WordPress Support site, they advise people to delete Cookies and the Browser cache and try again. This seems to work for quite a number of people. It didn’t for me.
So I searched around a little and found the problem: There was an exceptional rule to block Cookies for the domain wordpress.com. Once I deleted this rule, all is back to normal.