Maybe because Russia realized that Edward Snowden had a powerful name and they'd win favour with the lefties of the world if they protected him? That's one possibility. Or maybe because "let me try and be friends with the (perceived) enemies of my enemies." (although Snowden wouldn't characterize himself as an enemy of the US).

The important point is - a good thing done for bad reasons, might still be better than a bad thing.

Because he was stuck in the Sheremetevo airport when U.S. authorities remotely disabled his passport. He just ended up there. I think he was trying to go to South America or Cuba or something.

He probably chose Russia understanding that other countries would give him up sooner or later (does Assange story tell you anything?).