The last country to bear the name was the Federal Republic of Yugoslavia (FRY) established on March 27, 1992. It was a federation on the territory of the two remaining (non-secessionist) republics of Serbia (including the autonomous provinces of Vojvodina and Kosovo) and Montenegro. On February 4, 2003, it was renamed to the State Union of Serbia and Montenegro, and officially abolished the name “Yugoslavia”. On June 3 and June 5, 2006 respectively, Montenegro and Serbia declared independence, thereby ending the Yugoslav state. (From : http://en.wikipedia.org/wiki/Yugoslavia)
Hereby a short resume, by date:
Slovenia: 25th June 1991
Croatia: 25th June 1991
Macedonia: 8th September 1991
Bosnia-Herzegovina: 1st March 1992
Montenegro: 3th June 2006
Kosovo: 17th February 2008
“The Death of Yugoslavia”, by the BBC
A very good documentary from the BBC about Yugoslavia is “the Death of Yugoslavia” where the desintegretion is well described with interviews with all the main actors.
You can search for these BBC documentaries on youtube.