I traveled from Beijing to Moscow on the trans-Siberian train. It took five days.
One tip: if you're thinking of making the journey, bring a small hose with you so you can hook it onto the sink and have a little shower. Also, there are companies that will arrange home stays if you want to get off in Yekaterinburg or a few other towns and kick around for a bit.
In the early 90s, I traveled from St Petersburg, Russia to London's Victoria Station. I'm pretty sure the route does not exist any more, as it involved going through all the Baltics, Poland, Berlin, and eventually the Oostende-Dover ferry and on to London. All in all, it took about three days (including a 12-hour layover in Berlin).
One tip: if you're thinking of making the journey, bring a small hose with you so you can hook it onto the sink and have a little shower. Also, there are companies that will arrange home stays if you want to get off in Yekaterinburg or a few other towns and kick around for a bit.