What would cause your car to squeek constantly while you drive it?

A bearing, bushing or other rubbing surface has worn or dried out, or the brakes have worn down to the wear sensor. Either way, it's not a good thing. If the noise changes pitch when you touch the brakes, it's probably the brake wear sensor, get the brakes fixed right away. If not, it could be a dry wheel bearing, U-Joint (if your car has them), serpentine belt or who knows what else. Try to localize the sound. See what's causing it. Noises like that shouldn't be ignored.