Internet filtering is certainly one of the main tools available to control the internet. Nonetheless, the conditions in which it is done are crucial to ensure the balance between liberties and social needs. The Great firewall of China obviously does not create that balance; but France Germany and many other European countries have done so when filtering or banning racist websites, notably those denying the holocaust.
"Internet Filtering Appearing On Various Wishlists For Obama" (11 December 2008)
"Australian ISPs Refuse To Censor The Internet" (10 December 2008)
In comparison, I found the private filtering (by non ISPs; by private companies such as a shop or a newspapers) much more troubling and scary. "Online Video Sites Harming Themselves With Geographic Restrictions" (8 December 2008)
The help of the ISPs and other internet censors is crucial, so yes they should be responsible, but maybe in different terms, by analogy to public institutions' liability?
"Should Internet Censors Be Responsible For Breaking Stuff?" (10 December 2008)