If you are not running one of the browsers and versions listed at http://browsehappy.com/ please try upgrading or switching first.
If you are using an IE browser in compatibility mode please disable that mode. 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/
(1) Try clearing your browser’s cache http://www.google.com/support/accounts/bin/answer.py?hl=en&answer=32050
(3) Disable all browser extensions or add-ons temporarily.
(4) Try enabling HTTPS: http://en.support.wordpress.com/https/
Add both *.wordpress.com and *.wp.com to your list of trusted sites under the Security tab. Make sure to uncheck the box for “Require server verification (https:) for all sites in this zone.” http://en.support.wordpress.com/https/#frequently-asked-questions
(5) These are the accepted file types:
Instructions here http://en.support.wordpress.com/images/
Here are more details about the options for uploading images http://wpbtips.wordpress.com/2009/04/26/images-the-three-link-options/
troubleshooting images here > http://en.support.wordpress.com/images/troubleshooting-images/
If you are not successful let us know:
(a) How you are connecting to the internet and to WordPress.com.
(b) Exactly which browser (and version of it) you’re using by checking here if necessary http://www.whatbrowser.org/