Blocking web sites has been an issue for long time now. While carriers may offer URL filtering services, sometimes as a value-add service (for security or inappropriate sites for minors), some countries demand ISPs to block sites which present illegal material such as child abuse, or more recently, links to copyright protected material (US "SOPA" - here).
While many doubt the ability of ISP to block URLs (see "Ofcom: "All site blocking techniques can be circumvented" - here), some recent data (see below) shows that despite that, millions of web requests are blocked every year in some countries.
Nevertheless, in a recent case in Denmark, 8,000 sites were mistakenly blocked by a police officer who misplaced a list of sites (see "Police Censor Google, Facebook and 8,000 Other Sites by Accident" - here). See also a case in Argentina - here.
thejournal.ie reports on a proposal made to the Irish Senate "for a system to block internet users from accessing child pornography .. the motion [see below], which is being proposed by Independent Senator Jillian van Turnhout (pictured) and other Taoiseach’s nominees, could help cut the number of people in Ireland viewing images of child abuse .. The measures would block internet users in Ireland from accessing child abuse material hosted on servers internationally. Similar systems are in place in the UK, Sweden, Norway, Australia [here, here] and New Zealand".
The article provides some information on the activity of such systems in other countries: "Countries with similar systems had seen thousands of requests blocked, [Internet safety advisor] Pat McKenna added. “Norway has a population similar to ours. They block 10,000-12,000 requests a day .. In the UK, BT alone blocks 35,000-40,000 requests a day. That’s 58 million requests a year, just from one ISP".
See "Child pornography blocking system to be debated by Seanad" - here.