Are you trying to post via http://wordpress.com/#!/post/ or Posts -> Add New in your blog’s Dashboard? If you haven’t tried both, please try the one you haven’t tried.
If you are not running one of the browsers and versions listed at http://browsehappy.com/ please try upgrading or switching first.
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
If you are running one of the browsers and versions listed at http://browsehappy.com please do these four things:
1. Try clearing your browser’s cache http://www.google.com/support/accounts/bin/answer.py?hl=en&answer=32050
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/
If you are not successful let us know which browser (and version of it) you’re using and post any error reports you get.