I also had a similar problem. The blog on my wordpress.com account works fine, but one of the ones I'm hosting elsewhere won't let me log in.
The login page seems to accept my username and password (I don't get an error), but it does not send me on to the dashboard. However, if remove the query string from the URL, I get the dashboard. At that point, clicking anything takes me back to the login page. I found this page in the codex that had a solution that helped temporarily:
I use Firefox and have Zone Alarm as a firewall/anti-virus app. Following the directions for Zone Alarm fixed the login problem until I restarted the machine. Afterward, even though the settings in Zone Alarm were the same, the login problem returned.
With Zone Alarm disabled, I can log in, so I assume it's a firewall issue. That also seems to jive with what others have posted about it working from one machine and not another.
Obviously, having to disable the firewall to work in WordPress is not a satisfactory solution, but at least we are getting closer to figuring it out.