The only time you will get a stamp is on the Eurostar before you board. Everything else is a part of the schengen, so no border controls = no stamps.

That said, for places with border controls, usually, one of three things happen:
1. The train stands at the last station of country A until everyone is checked/stamped; same procedure at the first station of country B. Border guards walk through and you only need to present your docs when requested. It is, however, a good idea to make sure you have your passport before the train leaves the station.
2. Same as #1, but you have to walk out, get your thing stamped, and then they walk through, check to make sure everyone's stamped. Usually this is done because border guards don't have the necessary equipment, or the country is too cheap to invest in handhelds, or they don't work well, etc.
3. Two sets of border guards simultaneously move through the train between the last stop of country A and the first stop of country B. Train keeps moving.

I experienced all 3 within the past few years.

#1: On Kiev-Moscow train in summer of 2007, in the middle of the night. Both sets of guards did it this way, although the Ukrainians had handhelds, and Russians had to call in my US passport info over the radio. There wasn't a real customs check here, the train guy simply said that "nobody has anything" and they moved on. This was on one of the more expensive trains, though.

Also, between Turkey and Bulgaria a few weeks ago over Thanksgiving. The Bulgarian guard took the passports, went to an office with them, came back with stamps. Also in the middle of the night. Customs guys were pretty thorough: opened a few ceiling panels, looking for contraband such as cigarettes, although it seemed that more than half of the car was full of Americans and Japanese.

#2: Only in Turkey so far. You have to buy a visa if you don't have one, then go get stamped. They only have one or two passport scanners. Again, customs were thorough -- opened ceiling panels, etc.

#3: Between Prague and Dresden, also summer 2007. This was a mere formality, although I guess if you didn't have the proper visa, they could send you back on the next train (every 2hrs). No customs to speak of.


Also: you may see/experience random police document checks on trains. I experienced one between Munich and Salzburg in Jan of this year. Pretty harmless.