Generally, most tires have what is called 'wear-bars' molded into them and are placed regularly across the tread area of the tire. As the tire wears, these bars will be more and more visible.
If you are to the point where the bar is clearly visible without having to feel around, then it is time for your tires to be replaced.
If you are in the US, on trick to use is to take a penny and stick it into the tread 'head' first. If Abe's head is completely visible, then you are good to go, but anything less is a sign that you need new tires.