It's always tempting to try to squeeze a few more miles out of your rubber, but it's certainly not wise. You need to give your car what it needs to maintain proper contact with the road. Think of all you ask your car to do for you, every single day. Now imagine picking up the kids from school in a snowstorm wearing flip-flops, or taking the dog for a run while wearing stilettos. It's all wrong. Your feet need better equipment to get the job done. So does your car.
If you don't know how old your car's tires are (you bought your car secondhand, or you're not a meticulous receipt- or record-keeper) chances are you're probably due for a new set. Even if the tread looks decent, rubber deteriorates over time. The damage might not be easy to see, but miniscule cracks cause loss of structural rigidity, which means the tire can't perform as designed. If the rubber disintegrates where the tread joins the tire, the tread can separate (yup, just like a semi-truck). Not really worth taking the chance, is it?