One could even say it is becoming somewhat controversial. This was underlined at a recent meeting in Salonika, when members of the council's parliamentary assembly took the virtually unprecedented step of warning an applicant country, Croatia, to improve its human rights performance if it wanted full membership.
"Our main objective is to promote the core values of pluralist democracy," the council's Secretary-General, Daniel Tarschys of Sweden, told the Independent. "There must be certain minimal conditions to be fulfilled. We can't just take in any country."
Not much was heard of the council from 1949 to 1989, during which time its membership was confined to Western European countries. Its role in the Cold War was mainly to demonstrate how these states had embraced freedoms denied to the Soviet-controlled countries of the East.
Since the fall of Communism, however, the number of member-states has risen from 23 to 39 as new democracies in Central and Eastern Europe have flocked to join. Clearly, these states believe that membership matters, perhaps because it is taking them so long to achieve the bigger prizes of entry into the European Union and Nato.
Mr Tarschys, a former professor of Soviet and East European studies at Uppsala University, said Council of Europe membership was important to a Central or Eastern European state. It served as proof that the state was considered democratic; it showed the country was binding itself into free European institutions; and finally, for some new-born states such as Moldova, or the former Yugoslav republic of Macedonia, it underlined European acceptance of their independence.
Notwithstanding the recent warning to Croatia, the Council of Europe attracts criticisms from politicians and commentators who say it has turned a blind eye to some countries' failings in order to expand its membership as fast as possible. The most obvious example concerns Russia, which was admitted early this year despite widespread concern over the war in Chechnya and the quality of Russia's political and legal systems.
Another example involved Romania in 1993, when Hungary argued for delaying Romanian membership on the grounds that Bucharest was still discriminating against the country's ethnic Hungarian minority. In the end, Hungary abstained in the vote, allowing Romania to join.
Significantly, when the vote on Russia was coming up, President Boris Yeltsin publicly warned rejection of the application would damage Russian relations with the West. It was a sign of how seriously Moscow took membership of the council, an institution denounced in Communist times as a vehicle for Western propaganda.
Mr Tarschys acknowledges that some states, especially those with "an interrupted democratic tradition", such as the Czech Republic, Hungary and Poland, presented the council with few problems when they applied to join. "As we came further to the east, there were more doubts as to whether some countries were ready for membership. I pleaded for an inclusive strategy," he said.
The "better-in-than-out" argument rests not only on the assumption that it is easier to influence a country's behaviour when it belongs to the council. It reflects the view, put by Mr Tarschys, that the council's activities are "not just a finger-pointing exercise" but are intended to encourage reform.
A variety of new programmes are in place to help strengthen democratic institutions and the rule of law in Eastern Europe. One is a Council of Europe Youth Centre in Budapest, where young Europeans exchange ideas about human rights, political extremism, unemployment and other issues.
The council is also involved in the post-war reconstruction of Bosnia, for under the Dayton agreement the council was asked to help set up a Bosnian human rights commission and a constitutional court. A sign of the council's growing importance is that the United States, Japan and Canada have all recently requested, and been granted, observer status.