re: What does Russia get out of propping up the Assad regime?

Primarily, influence in the region. The conflict in Syria/Iraq is the best-selling show in town right now and there are some chips in play with the regional heavyweights. The GCC powers and Turkey (Western aligned) are anti-Assad, so Russia backing Iran and the Shia is kind of a natural fit. And it's not completely bare-bones. There are some historical ties there.

My views on it are a bit complicated. I'm extremely distrustful of the Sunni powers we call friends (really with the exception of Jordan) and think that [continued] engagement with Iran could pay dividends in the not-too-distant future. Furthermore, I believe, in general, that we're better off with detestable secular leaders than with faith-driven fanatics of any kind. But Assad is a real PoS. He brought most of this on himself.