The UN doesn't "recognize" countries, it just happens to have most all countries as members. The official list of UN members, containing 191 countries, is here:

http://www.un.org/members/

Note that some countries voluntarily choose to stay out (the biggie for a long time being Switzerland, but they'd finally joined so the sole holdout seems to be the Vatican now), and others are just "entities who have received a standing invitation to observe" (!), including Palestine and the Sovereign Military Order of Malta (whose territory consists of an office in Rome).