What causes blood to not clot?

Antithrombin: The body has a complex system of clotting and anti clotting cascades. The principle anticlotting proteins are Antithrombin which in turn requires other cofactors to function properly. Once a clot begins to form, plasmin becomes activated which breaks down clot. Whether a clot forms or not is a race between the pro-clotting and anti-clotting pathways.

Balance: The body has a natural ability to form and prevent clots. This balance allows us to clot when we are cut and keep the blood thin to avoid strokes etc. Medications are used to enhance the desired effect.