by Michael Kelly - Business Insider - There are three primary reasons, as illustrated by this report by Krishnadev Calamur of NPR. 

1) Strategic: Syria's port of Tartus hosts the only remaining international military base outside of the former Soviet Union.

2) Financial: As of June 2012, Russia’s economic interests in Syria total approximately $20 billion, about $5 billion of which are weapons sales. 

3) Philosophical: Andranik Migranyan, director of the New York-based Institute for Democracy and Cooperation, a nongovernmental organization funded by private Russian donors that is considered close to the leadership in Moscow, told NPR's Robert Siegel: "Russia's position is very easy to understand."

"First, Russia is against any regime change from outside of Syria or any other country because according to Russia, any attempt to change the regimes, they are ended up in a chaos and results are quite opposite what were the intentions," Migranyan said. "This was proved in Iraq after the invasions of Americans over there. This was proved in Libya. This was proved in Egypt. And Russia is against principally this regime changes."