If you are concerned about health and safety issues then you should get travel insurance. If you are a European citizen then the chances are you already a health insurances card from your own country which would cover you in all European states.
If you come from American, Australia or somewhere outside of Europe then you would need your own insurance. In Ireland there is a very good public health system and if you have an accident then Irish Hospitals will take you in. On the Aran Islands there is a resident Doctor and Nurse. If you have an accident or need medical attention they will come to you straight away and look after you. Depending on the severity of the issue then you may need to take helicopter to hospital which is available for medical emergencies to take you to the Hospital in Galway or Limerick.