Mountain Lion upgrade and many sites are not opening
This issue affected several people after upgrading to Mountain Lion. For many, reducing their MTU size solved the issue:


Open System Preferences.
Select Network.
Select your connection and choose Advanced...
Select Hardware.
Change Configuration to Manually
Reduce the MTU size to 1300. Most people had good experiences with this value.
Observe how ping behaves over time. You can further reduce the MTU size in steps of 4.


However, there seems to be another issue: Proxies. The solution suggested here is:


Open System Preferences.
Select Network.
Select your connection and choose Advanced...
Select Proxies.
Turn off Auto Discovery Proxies.
Apply the settings.


This should be fixed with an upgrade to OS X 10.8.1 (not sure if an upgrade to Mountain Lion directly brings you to the latest upgrade, or to 10.8.0).

Actually, I would first try the upgrade to 10.8.1. If this does not work, try the proxy solution. If this does not work, try the MTU size reduction.