Tires must be replaced when the tread is worn down to 2/32 of an inch in order to prevent skidding and hydroplaning. An easy test: place a penny into a tread groove. If part of Lincoln's head is covered by the tread, you're driving with the proper amount of tread. If you can see all of his head, you should buy a new tire. Built-in treadwear indicators, or "wear bars," which look like narrow strips of smooth rubber across the tread will appear on the tire when the tread is worn down to one-sixteenth of an inch. When you see these "wear bars," the tire is worn out and should be replaced. Visually check your tires for signs of uneven wear. You may have irregular tread wear if there are high and low areas or unusually smooth areas. Consult your tire dealer as soon as possible.
If your car develops a shimmy (a back-and-forth vibration, usually felt through the steering wheel) at a certain speed, it's possible that one of your tires has lost its balance weight. Having your tires re-balanced is a fairly inexpensive job.