The tread on your tires should never fall below 1/16 of an inch (1.6 millimeters) in depth. If you regularly drive on slick, wet surfaces, you'd be even better off with twice that much. You can buy a gauge to measure the tread depth the way the professionals do, but there's an old trick that will give you a rough idea of how much tread depth you have left and it won't cost you more than a penny.
In fact, it requires a penny. Take a Lincoln-head penny, the kind you find in your change every day, and insert Abe's head (head-down) into the tread. If Lincoln's entire head remains visible, you don't have enough tread. Take your car into the mechanic and ask about getting a new set of tires.