You sometimes see inexperienced runners looking at the bottom of their running shoes to see if it needs replacing, for example by seeing whether it has much 'tread' left. This is a mistake: the main determinant of the longevity of a shoe is not the wear to the outer sole; it is the compression of the mid-sole, which is the spongy layer between the outer sole and your feet.
The material that is usually used to make mid-soles is light and absorbs shock well, but it gradually compacts as it is used, which reduces its shock absorbency and gradually distorts the shoe.
As a result of the compression of the mid-sole most running shoes have an average life expectancy of about 300-600 miles. Very heavy or uneven runners might wear out part of the outer sole before the mid-sole is too compressed, but this is unlikely.
The actual life of your shoes depends on your weight and your running style. You can see whether your shoes are past their best by looking at the compression lines along the side of the shoe, and seeing whether the mid-sole can be compressed with pressure from your thumb.
If you can no longer compress the mid-sole, then it is time to replace your shoes. If you begin to get any kind of ache or pain in your ankle or knee, check that your running shoes don't need replacing.
Incidentally, you should not put your running shoes in the washing machine, nor use very hot water to clean them. The hot water damages the shoe, especially the mid-sole, and leads to distortion in the shape of the shoe. For the same reason, you should avoid drying wet shoes on a very hot radiator.
Many runners keep track of the life of their running shoes in their training log, and use this to warn them when they are likely to need a new pair.