If one considers a few historical and strategic facts, one could make the argument that Russia's Putin would be a fool NOT to invade and annex the Crimea.
The Crimea became a part of Russia - not Ukraine - in 1783, nearly as long ago as the US colonies broke away from England to form the USA.
During the years of the Soviet Union, when ALL decisions were made centrally in Moscow, both Russia and Ukraine were part of the Soviet Union.
In 1954, the Crimea, after being part of Russia for 171 years, was administratively transferred by the Soviet Union's Moscow dictators to the Ukraine. The population of the Crimea then as now was overwhelmingly ethnic Russian and/or Russian speaking.
The Crimea is of huge strategic and military importance to Russia. It is the home base of Russia's only warm water naval base.
But for the 1954 administrative decision made by a handful of Soviet Union Communist dictators in Moscow, the Crimea today would still be part of Russia and not part of the Ukraine.
Based on the above, one could see how Russia's Vladimir Putin would decide that he has to invade and annex the Crimea, to protect Russia's national security interests.
It may not make it "right" and it is certainly not the preference of either the Ukraine government in Kiev, the European Union or the USA, but his actions have a certain logic.