I think if it weren't for Brezhnev's stagnation, the Soviet Union could have enjoyed the good economics that happened under Khrushchev. If one of his successors took over in, say, 1970, instead of Brezhnev, and was then replaced by Gorbachev in 1985, the people in the non-Russian republics might actually want to stay with the Soviet Union.
In 1991, the USSR adopts a new constitution, based on Gorbachev's liberal polices. The nation is ready for such a change, and the "Unbreakable Union" indeed endures. An election is held at the end of the year, and Gorbachev is elected President (or General Sectary) of the Soviet Union. Low and middle level elections are also held in the regional "Soviets," and for the first time since 1917 the people actually choose their own leaders. In some republics, there are calls for independence, but they are overshadowed by the reality of the successful economy, amongst fears of Western domination if such wishes became reality. The people in the republics are satisfied with their new government, and ultimately decide to stay with the Soviet Union.
The result? If things go well, that area of the world won't be so crappy. the smaller republics would have the benefits of being part of a large, strong nation, and the larger republics wouldn't have so much chaos. Perhaps the Soviets would endorse a somewhat socialist blend of free-market economics, similar to those of Japan and Western Europe. Politically, the Soviet Union could continue to counterbalance the power of the United States while worked towards better relations between both nations), and thus the whole Iraq war could be avoided.
Around, the whole world, the influence of not one, but two democratic superpowers could be a blessing. The problem of the unipolar world could be avoided, thus allowing people around the world to feel more secure (since the US wouldn't have such overarching authority), with neither the US or USSR being able to wield such power over the entire world (since they would geopolitically counterbalance one another). This would encourage medium-sized nations to gain more standing in their respective regions, without the constant threat of the United States in the way.
This is not to say that there would be no foreign intervention when one nation attacks another (i.e. the Gulf war), but simply that it wouldn't just be one single nation (in this case the US) "deciding" who can have nukes (Israel & Iran), who can attack who (okay for Saddam to invade Iran but not Kuwait), among various other things.
Okay, I'm rambling.