Oh, wow! Thanks for that, GEST!

Boris Grebenshikov is sort of the Russian Richard Thompson.
One of my favourite albums is Chubchik, a collection of (mostly) traditional Russian songs from the 20s and 30s.
http://aquarium.lipetsk.ru/MESTA/mp3/aquarium.ru-albums/chubchik241.html

Another fantastic album is the Russkiy Albom (Russian Albom), entirely original rock songs, but based on traditional Russian motives with Indian influences. There are even some bagpipes!!!!
http://aquarium.lipetsk.ru/MESTA/mp3/aquarium.ru-albums/russian_album.htm

Some other good albums are his covers of Vertinsky (the Russian Pierott) romances and the covers of Bulat Okudzhava, the bard.