One of the states which chose to leave the Commonwealth was Ireland, although it did not do so until 1949, when the government of John A. Costello repealed the External Relations Act and declared Ireland a republic. For the first time, all formal links to the British Crown were abolished (they had been abolished in practice by Eamon de Valera during the 1930s), and the state withdrew from the Commonwealth. It was admitted to the United Nations in 1955, and to the EEC in 1973.
There are those in Ireland who favour re-entry into the Commonwealth, given the much improved nature of our relationship with Britain, although this is very much a minority opinion. The Commonwealth is seen as a hangover from the bad old days of empire, and increasingly irrelevant given the state's membership of the EU, a much closer grouping with much more tangible benefits.