And the answer will be “Very deep”. But it all depends on personal circumstances.
If you come from nobility stock then you might be in luck. Famous nobility families have been researched by various genealogists and historians. Books are written about them and their family trees are published on internet. Yes, this is true. Go to http://www.rodovid.org/ and you will find there big nobility trees with lots of branches. For example, the family tree of Bagrationi has been traced to as early as 1300s.
If you come from peasants, then the answer will be “Yes” again. If your ancestors lived in the same village for many centuries and most importantly the archives have the records from ancient times, then you might be in luck. I remember watching a TV documentary on a Russian celebrity where his peasant family tree was traced for 8 generations.
If your ancestors were of Russian Jewish heritage, then you might be in luck again. Jewishgen.org has a great collection of archival records. For one of my clients, I was able to reconstruct one family branch up to 1810s. However, the other branch did not go further than the great-grandfather only because the records have been lost in wars.
For most Russians and people with Russian heritage, the answer to the question ”How deep can you dig?” will be “Shallow”. The ancestry and family heritage topic has been prohibited in Soviet times. Grandparents tried to hide any information and parents simply did not know anything. So there is nothing to pass except for short stories, rumours and legends which have been created over time.
But not everything has been lost in Russian archives. Even so there are no databases as ancestry.com and familysearch.org, the Russian archives are full of documents and information and it is possible to research your Russian genealogy. You just have to know where to search.
The process will be in some cases costly, long and frustrating with nothing on your ancestors. But it might be a completely different experience and bring quick results. On my website I publish lots of interesting information and tips on where and how to search, cover specific topics and most importantly stories of great success. May be one of these stories will be yours. Contact me and I will guide you.