Since Montenegro became a member on June 28, 2006, the United Nations comprises 192 of the 195 states it recognises. The only non-member states are Vatican City (which is however a permanent observer) and the Niue and Cook Islands. Those islands are juridically self-governing states in free association with New Zealand, and as non-sovereign states they cannot become members.
Vatican City is thus the only fully recognised independent state which is not a member of the United Nations. Actually, nothing could prevent Vatican City from becoming a member of the U.N. if the authorities decided to apply.