The cities are pretty safe, with common sense being the only precaution needed. However, do watch out for the monkeys in Lopburi. They are a cheeky bunch and have been known to steal anything that you can't hold onto, from your coffee cup to your camera.
Rubies, brought in from Burmese mines, are a big draw at Mae Sot, but unless you know what you're looking at, you might find yourself with substandard or fake gems, as scams on unsuspecting visitors are common.
Periodic clashes between the Thai army and the government of Myanmar (Burma) occasionally result in the closure of areas along Thailand's western border. Check the State Department's Web site (travel.state.gov/travel/travel_1744.html) for updates.
Motorcycle thieves who ride up alongside other motorcyclists and snatch their bags are a problem in central Thailand.
In an emergency, contact the Tourist Police first at 1155.