If you walk onto the train with a ticket you printed, I don't think I've ever been asked for an ID. I might if I were picking up a ticket at the station.

You definitely need ID for hotels a lot of the time. Not sure the level where the regulations are put in place--probably varies--and Europe is probably more formal than the US in this regard. Was staying with a friend in Europe about a year ago and they had to take our passports to the police station to make us "official."

As I wrote elsewhere, I also had a challenge in the US a few years back but I expect that, had I been at my usual chain, there would have been a discussion with the manager followed by "I see nothing, I hear nothing."