However there are five "difficult" cases in this. Namely Palestine and Kosovo, which both do not have enough international support to become a United Nations member, and for Palestine it is a controversial topic by itself whether it is a separate country or not. Taiwan left the United Nations in 1971 when the Republic of China got a seat. South Sudan recently became independent and therefore has not yet applied to be a member. And the Vatican City has chosen themselves to not become part of the United Nations.
So to answer your question, only Vatican City is by choice not a member of the United Nations. However it does enjoy full observer status.