What are the causes of ruptured blood vessels in the eye?

Depends. Depends on which ruptured vessels -- surface conjunctival vs. Inside the eye (retina). Should be examined by an eye care provider.
Many. The most common cause of a conjunctival hemorrhage is dry eye. This can be worsened by use of anticoagulants such as Aspirin or coumadin (warfarin). Rarely, the burst vessel may be due to extremely high blood pressure or clotting problem. If you have a headache or the hemorrages are recurrent, be seen soon.