Kosovo
When is a country not a country?
Kosovo, like Slovenia, Croatia, Bosnia and Macedonia, broke away from Yugoslavia in the early 1990s and declared its independence. Unlike the others, it didn't stick and was only recognised by Albania.
Part of the problem was that Kosovo is ethnically mostly Albanian, but historically it is very much part of the Serbian national identity - the Battle of Kosovo in 1389, despite being a defeat for the Serbs against the invading Ottoman Turks, is still a matter of great national pride.
At any rate, a campaign during the 1990s of peaceful resistance turned nasty after the Dayton Agreement (sorting out the war in the rest of Yugoslavia) didn't address Kosovo. Realising that the West just wasn't interested, the Kosovo Liberation Army started a rather more ... active campaign of resistance. Slobodan Milosevic's Serbian army (well, technically Serbian/Montenegrin) responded, and the result was the NATO bombing of Serbia in 1999.
Kosovo went into UN administration for the best part of a decade, with any attempt by the West to conclude independence being stymied by Russia in her traditional role as "Big Bro" to the Serbs.
Eventually, in February 2008, Kosovo declared independence - however to date only 85 countries have recognized it. All of NATO has (except Spain, Romania and Slovakia, because all of them have independence movements back home: Basques in Spain, Hungarians in Slovakia, Székely/Hungarians in Romania), Russia has declared the independence to be "illegal" and China is passively supporting the Serbian side. Kosovo has wisely not applied for UN membership. On 22 July 2010, the International Court of Justice issued an advisory opinion after Serbia requested it that the declaration of independence was legal, which the International Court confirmed it was because there is no law that prohibits the declaration of independence.