Please provide some specific information so we have something to work with as without it we can't help you.
(1) How you are connecting to the internet and to WordPress.com?
The way you connect to the internet (mobile, satellite, DSL, dial-up) and to your blog, and how many proxy server jumps etc. it takes to connect can cause problems. There maybe be problems with your ISP and/or with the proxy servers. Also note that the main dashboard isn’t designed to work with touch devices through the tablet and smartphone browsers.
(2) Are you using the secure https:// login?
(3) Exactly which browser and version of it are you using. If you aren’t sure click here to find out > http://whatsmyuseragent.com/
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
Have you done any troubleshooting? Below are the troubleshooting steps we take whenever any issues like this arise and undertaking them will provide valuable feedback information for Staff:
a. clearing your browser cache and cookies > http://www.google.com/support/accounts/bin/answer.py?hl=en&answer=32050
b. Using the browser with all extensions or add-ons disabled
c. updating the browser to the latest stable version (not a buggy BETA browser version) http://browsehappy.com/
d. Confirming third party cookies is enabled on the browser http://support.google.com/accounts/bin/answer.py?hl=en&answer=61416
f. Confirming Flash is updated http://www.adobe.com/software/flash/about/ and if required installing the latest version of Flash http://www.adobe.com/products/flashplayer/
g. Resetting your router and modem and rebooting your computer
then logging in using the secure https:// log-in
h. Trying another browser