The United Nations was initially chartered in 1945 with 51 member nations. Its current membership is 193 nations, which are all represented in the General Assembly. While the list of these nations is obviously too long to ennumerate in this space, there are fifteen member nations that make up the UN Security Council, the most important decision-making body of the United Nations. Five of these nations are permanent members. They are the United States, the United Kingdom, Russia, China, and France. The other ten members are elected and rotated through on two year terms. The current members are Azerbaijan, Colombia, Germany, Guatemala, India (term expires this year,) Morocco, Pakistan, Portugal, South Africa, and Togo. Important matters, including those requiring military action, must have the unanimous approval of all five permanent members plus at least four elected members.
The main reason of the incapacity of the UN to solve the main problems in the world is the right of veto the winners of the WW II appropriate to themselves.
The interests of these big countries being opposite, the veto of only one of them paralyses the whole organization.
See the war in Yougoslavia in the 90ies, the actual war in Syria etc.
The United Nations has at least 190 members. That was the number in 2002 when Switzerland became the 190th. The better question might be to ask what countries are not members.