This is the famous 6 day train ride that spans 9,000 Km and 8 time zones from Moscow to Beijing. This route is 
actually called the Trans-Mongolian, because it passes through Mongolia after turning south at Lake Baikal 
(deepest fresh water lake in the world).  My opinion of being on a train for 6 days is that it all depends on the people you meet.  If you're alone, and no one speaks your language, you better have brought a couple books.  However, the ticket office seems to put foreigners together in the same train cars, so your chances of having a good time and good conversation is high.  I brought 5 books, but never got the chance to open more than 1.  Not everyone is going all the way, so some of your friends come and go, but between meeting people, sharing stories, and at least one night of drinking vodka with the Mongolian or Russian passengers, you'll feel as if this is what you've come to see... and you're not even there yet!

The scenery changes very slowly in Russia.  the first 4 days out of Moscow look the same.  Lake Baikal is exciting because this huge lake is a major change in scenery.  Between Lake Baikal and Beijing, however, the scenery changes a lot.  There's forests, mountains, rolling green hills, sandy desert, rice paddies, and or course the Great Wall.

When not socializing, there nuance of being on a train always provides you with something to do.  There is a dining car for each country you pass through, serving local specialties, and some basic western foods.  But most people (like me) stock up on instant noodles and various other non-perishables before they get on the train.  There is a hot water boiler in each car called a samovar from which you can always pour yourself hot water for tea, instant noodles, soup, or whatever else you have to re-hydrate.  If you don't have a weeks rations with you, every train station you stop at is filled with food sellers (and beggars) who can help you stock up.

The next most exciting thing is anticipating the train stops.  On the Southern side of the tracks are white mile markers.  If not you, someone is bound to have a Lonely Planet which can help you navigate this 9000 km journey, so you can always know where you are, and what's coming up next.  If you plan on seeing anything significant, you best stick to this method, because the sights come and go quickly, and everything between looks pretty similar.  Such "sites" include towns of note, the dividing marker on the Europe/Asia border, monasteries, historical structures, and markers preparing you for the upcoming train stop.  The train stops only once every 5 hours, and sometimes the stops only last 5 minutes, so if you need something from the platform, you best be prepared as soon as the train pulls into the station.

There are 3 classes available.  Second class is cheapest, and will probably allow you to meet more backpack travelers.  First class is as nice as it gets in some trains, but in other trains (such as mine) Premium class is available.  Premium class means 1 thing - showers!  No, there are no showers for this 6 day journey unless you get Premium class, so be prepared to get very comfortable with you cabin mates.  Second class has 4 berths to a room, while 1st and Premium have 2 berths.  The Premium class is supposed to offer air conditioning in the summer, but on our train it was broken.  And don't think summer in Asia is cool.  Our room turned into a literal sauna in the morning while going through the Gobi desert.  And on that last day in China, everyone was leaning out the windows to escape the heat as much as to see the Great Wall.