The Crimean parliament has scheduled a referendum for March 16 asking whether Crimea should secede from Ukraine and join Russia. From the standpoint of international law (Ukrainian law may be different), it is not illegal for a territory of a country to attempt to break away and form a new state. But there is a great deal of controversy over when a breakaway territory should be considered a state, which entitles it to enter treaties, join the UN, and so on. One view is that Crimea becomes a state just when other countries regard it as a state. So even if Crimea achieves de facto independence and has a government that controls it, the United States and other countries could block it from being a state just by refusing to recognize it as a state.
On another view, a breakaway territory is lawfully a state based on objective facts–basically, whether it has a government that controls the people who live on it, and is not itself subject to a superior government, as in a federalist system. In practice, these two views tend to converge. Sooner or later, foreign countries will recognize a de facto state as a de jure state because if they want to deal with the people who live in the territory (for example, trade with them), it must go through their government. That’s what happened with East Germany, for example. The west refused to recognize it as a state for many years because they considered its creation illegal but eventually gave in.
In the Crimea case, there are a number of relevant considerations. Favoring secession, one can point to the fact that the Crimea has long enjoyed a great deal of autonomy from Ukraine; that Crimea has long been part of Russia (or the Soviet Union) and was handed over to Ukraine only in 1954; and that, if the referendum succeeds, then the Crimean people themselves wish to secede.
Going the other direction, Crimea is currently occupied by Russian troops, and the question of secession was (as far as I know) put on the agenda only because of Russia’s illegal intervention. Unlike places like Quebec, the Basque Country, and Scotland, the question of secession is entirely new; there was never a live secession movement that sought reunification with Russia. Ukraine itself does not appear to favor secession of Crimea. The world ought to be skeptical about the Crimean Parliament’s intentions, but if a fair referendum is held, and there is overwhelming sentiment in favor of unification with Russia, then a major geopolitical victory will be within Russia’ grasp.
Update–maybe for this reason, President Obama has declared that the referendum would violate international law. On what basis? Perhaps that it would violate Ukrainian sovereignty, especially if the Russians are behind the scenes. But it wouldn’t be a violation of international law for Illinois to hold a referendum on whether to secede from the Union, and so I don’t see how it could be a violation of international law for Crimea to vote to secede.