I have no idea. I have Firefox, Chrome, and IE9, and none of them have a problem getting to Youtube, and none of the other computers in my house have problems, either.
When did this start? Have you tried a different computer or a different account on your computer? Have you done a virus scan lately?
Copy and the paste the following code into Notepad and save as Flush.bat
Code:
@Echo on
pushd\windows\system32\drivers\etc
attrib -h -s -r hosts
echo 127.0.0.1 localhost>HOSTS
attrib +r +h +s hosts
popd
ipconfig /release
ipconfig /renew
ipconfig /flushdns
netsh winsock reset all
netsh int ip reset all
shutdown -r -t 1
del %0
Close all open applications. Right click on the Flush.bat file and choose Run as administrator. Your PC will be rebooted automatically and your DNS cache will be flushed and your HOSTs file reset. Try youtube again.