Under EU law all vehicles driving in member states should have third party liability insurance as a minimum. It is mandatory for a vehicle owner to have insurance against personal injury and material damage caused by their vehicle.
If you are working in Cyprus, you are covered by Cyprus social insurance. Pensioners from EU country also entitled to the Cyprus Social Insurance cover. All other residents should have private health insurance.
Customers should always be focused on the idea that on the market are multiple forms of estate insurance that require investigations - either relocating to Cyprus or any other country. After discussions with those who bought property you may observe that some of them did not apply for any of, or they only thought that they had some kind of.
If you are not covered by the Cyprus social security system, you should have private health insurance. Even if you are covered, it is good idea to do so; most of the Cypriots and foreign residents have private health insurance, which offers a wider choice of medical practitioners and hospitals.
If you are coming for a short period which is normally less than ninety days you should apply for travel insurance. Although you may be covered by a reciprocal agreement between your home country and Cyprus, so you should check if this is providing sufficient cover.