Tito's Yugoslavia was 'non-aligned' after they broke from the USSR in 1949 (correct me if that's the wrong year). In those days, the term "third world" described non-aligned countries that were attached neither to the West nor the Soviets. Yugoslavia labeled themselves as "market socialism", a sort of hybridized third way between the West and the Communist East.

As such, they had somewhat of a favored status with the West, and were seen as an alternative, West-friendly model to the Communist Bloc. When the USSR fell in 1991 and was quickly subjected to "shock doctrine" liberalization, Yugoslavia's status wasn't so special or needed anymore, and Western support dried up.

Also, when Tito died in 1980 (I believe it was), political succession became a problem. Yugoslavia was very much a multiethnic federation, and he was the glue that held it together. (He himself was half Slovene, half Croat.) Underlying ethnic and economic tensions came to the fore, and bubbled over in the early 90s when first Slovenia and then Croatia (the two richest republics within Yugoslavia, whereas political and military power were concentrated in Serbia) opted out. The Serbs let Slovenia go without much of a fight (and Macedonia slipped out without any fight at all), but because Croatia and Bosnia had significant Serbian minorities within their territories, outright war broke out as the Milosevic regime in Belgrade wanted a unified "Greater Serbia" in the wake of Yugoslavia's impending demise.

That's the short, basic answer from a non-specialist. Search the archives and you'll find a whole, whole lot more.

It more or less worked for 73 years. Unification had been down to the identification of northern Serbs with their cousins in the expanded pre-war kingdom and Croat linguistic affinity, Slovenes joining out of a shared Slav identity. Tensions were visible from the 1920s, culminating in the Croat-Serb conflicts of the nazi occupation period.

Similar nationalist movements surfaced after the Soviet collapse in 1989-91: Czechoslovakia split in 1992, while Ceaucescu's fall was triggered by Hungarian minority protests. But Yugoslavia's final undoing wasn't a purely home-grown affair: from western recognition of secession in 1991 to military shipments in 1995 and and later overt intervention the knives were clearly out.

Did it have to happen? No. Other countries have managed minority aspirations without complete fragmentation, and the Tito regime had gone out of its way to allow autonomy and limit Serbian dominance (a reason for later Serb nationalism under Milosevic). Though the system was under the control of the ruling party, there seems no overriding obstacle to its evolution into a more liberal federal regime.

Yugoslavia's tragedy was that in the end nobody wanted it, neither nationalists in seceding republics nor the powers that enjoyed unique dominance in the 1990s, nor ultimately Belgrade itself.

/u/Chernograd gives good answer, but what you also need to take into account is, that almost every nation within Yugoslavia started to feel, like they're getting the short end of the stick in the late 80's.

Slovenia and Croatia felt, like all of their money goes towards less developed states like Bosnia and Serbia.

Serbia felt like Tito-Kardelj rule that was pretty much in power since the beginning of Yugoslavia, but was especially obvious post-1974, when the new constitution, defined the so called self-managing socialism. Self-managing socialism called for a "progressive" whithering of the state and of its power. That is the "party-officials" would slowly step down and the workers unions would take control and it would probably also mean disbanding, or at least changing how the military works. The 1974 constitution also had autonomy clause and the the option to freely exit the union, which was seen as Kardelj's (writer of the constitution) gift to his home state of Slovenia.

You also need to take into the account, that on other hand Yugoslavia had one of the largest military in the world, and that most of the higher-ups were either Serbs or Montenegrins. This, especially after the death of Tito, created a friction between Slovenian Socialist Youth (probably Croatia to a degree as well), who has not only completely adopted the ideas laid out in the Kardelj's 1974 constitution, but thought, that he didn't go far enough. They also likened the conservative high party officials and the top-brass of the military with fascism and nazism.

This led to things like "poster affair", when NSK did a poster for relay of youth, which took an nazi poster and swapped nazi imagery with yugoslav. Another "bout" between Slovenian Socialist Youth and the military came from, when the magazine of it called Mladina published some leaked documents about the defences and stuff.

Long story short, this coupled together with renewed Serbian nationalism, in the less than perfect economic environment, meant that Yugoslavia was destined to fail.

I wish I could find any English sources, but can't find any.