As you may have guessed from my name, I was born and raised in Russia. (I lived in the city of Novosibirsk until I was sixteen and a half). My family then moved to Bulgaria, and we immigrated to the States when I was 19. After immigrating, I, like most immigrants, went through a couple of stages of adjustment: from wanting to act and be treated as American as possible to eventually coming to realize that my Russian origin is not something to be ashamed of, and seeking out the parts of Russian culture I enjoy. Here, then, are the results of that search so far:

Russian Forever
Created by Mariya Shkolnikova, herself a Russian immigrant, this site has links to three other sites also created by Mariya Shkolnikova. I highly recommend all of them. You will probably enjoy these sites most if you are able to read Russian and understand it when it's spoken (or, more to the point, sung).
lib.ru
A very good (and growing!) collection of Russian fiction as well as well as non-fiction; "humanities" comprise the bulk of the non-fiction section. Again, you will probably enjoy this site most if you can read Russian.
bards.ru
An excellent site if you like Russian "author song." Again, the site is in Russian.