Former Soviet satellites and Russia itself I have heard bad things. Avoid wandering around in areas where you might become some Muslim terroist's next head-body separation project. China and most of Asia that I know anything about, no problems, and I have ridden night trains in Taiwan, China, and Malaysia. I have ridden day trains in southern Thailand and South Korea and long distance busses in Malaysia and the Philippines, and never had any trouble, but then I try to be polite to all, dress appropriately for the society, don't ask for special favors, don't flash money around. I usually have a camera on these trips, but I don't go around wearing a couple of thousand dollars of electronics or do other things to put on the "I am an obnoxious chump, please rob me" sign.
State Department warnings have to be taken with a grain of salt, sometimes a whole bag of it. They operate on the theory that it is better to give a useless warning than to miss one they should have. Just don't do stupid stuff. Most of the westerners that I know that have had bad experiences had set themselves up by being in bars late at night, out on the street drunk, trying to pick up local women, etc.
