Besides countries with on-going wars -- Yemen, Syria, etc -- or barely-there gov'ts (Iraq, Somalia) or both (Libya, Afghanistan), the only "stable" countries that come to mind where I would be wary of going are Pakistan, Mexico, probably Honduras and North Korea. While I'm sure there are nice areas in these countries, they strike me as potentially violent and unsafe.
Most countries go out of their way to be helpful to tourists. Thailand, a land with many corruptions, even has a Tourist Police bureau operating throughout the country. One of the best things about China is the safety level. There aren't any bad or dangerous sections of Shanghai. You can walk down any street past midnight alone. Nobody has guns (except the poorly trained armored car guards and the People's Armed Police, a counter-riot agency you rarely see in public). While crimes against foreigners are generally given a high priority, and criminals know that. At most there is a pickpocket problems, but little violent crime.
Also, many countries have fairly well-trod tourist routes and tourist zones which tend to be well-policed and safe. The worst I've experienced abroad is food poisoning (Kenya, Vietnam, Morocco) and minor hassles. Can't really think of any significant problems. Here and there someone might have been rude or tried to cheat us a bit on price. Stuff you get over in a few minutes.
And often enough you run into unexpected hospitality such as when our Palestinian taxi driver/guide asked if it was okay if we stopped at his home. And so we wound up hanging at his house for half an hour drinking tea and meeting his young sister, wife and newborn baby. Sometimes the informality is nicely refreshing, such as when our Jerusalem taxi driver asked if it would be okay if he stopped for 2 minutes to pick up a jacket from a tailor that happened to be near our hotel. Hell, in Tbilisi Georgia our car rental company was a big fat wrestler looking dude with 5 vehicles on the street, who was amused when I wanted to add in the price per day on his one page Xerox contract.
Poll
5 (45.5%)