We need some details please.
1. How are you 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. It sounds like there could be a problem with your ISP. Can you access any of these directly?
2. Are you using http:// log-in or are your using https:// see http://en.support.wordpress.com/https/
3. Exactly which browser(s) and version(s) of them are you using? If you don’t know click here to find out > http://whatsmyuseragent.com/
4. Have you tried clearing your browser cache and cookies? http://www.google.com/support/accounts/bin/answer.py?hl=en&answer=32050
5. Is your browser version up to date? You can upgrade any browser version here. http://browsehappy.com/
6. Have you tried using the browser with all extensions or add-ons disabled?
7. Do you have third party cookies enabled? http://support.google.com/accounts/bin/answer.py?hl=en&answer=61416
9. Do you have another browser you can try?
10. You can use this link to see if your Flash is up to date. http://www.adobe.com/software/flash/about/ If it’s not up to date then this is where to download and install the latest version of Flash. http://www.adobe.com/products/flashplayer/
11. Have your tried resetting your router and modem?