I'm not experiencing this issue. If you are not running one of the browsers and versions listed at http://browsehappy.com/ please try upgrading or switching.
If you are, please do these:
(1) Try clearing your browser’s cache http://www.google.com/support/accounts/bin/answer.py?hl=en&answer=32050
Note: If you are using an IE9 browser in compatibility mode that makes it render as IE7 and IE7 is not supported. To disable see > http://www.sevenforums.com/tutorials/1196-internet-explorer-compatibility-view-turn-off.html
(2) Make sure that you have third-party cookies enabled http://en.support.wordpress.com/third-party-cookies/
(3) Try with all browser extensions or add-ons temporarily disabled.
(4) Try enabling HTTPS: http://en.support.wordpress.com/https/ and try logging in directly to your own blog rather than logging in on the WordPress.com home page.
If it’s still happening, let us know which browser (and version of it) you’re using and post any error reports you get.