Currently there are 7 audiobooks in Russian, more are being added. There are no transcripts, but Project Gutenberg Online Book Catalog | Project Gutenberg has some of them.
Winnie the Pooh chapter 1 in Russian and English.
The best resource I have found for listening to are the Princeton University’s old SLA101 and SLA105 courses. They are getting harder to track down these days as they are no longer on the Princeton server. Try this link: http://www.freelanguagecourses.com/category/language/russian/.
I have e-mailed the author, he is a very generous man and is happy to let people use his materials for teaching themselves Russian. Drop him an e-mail if you use his materials, tell him they rock!
For complete beginners there are the Spoonful of Russian podcasts from Natalie at http://speakrussian.blogspot.com/. She’s apparently taking a break at the moment, but it’s worth looking through the archives.