As a student you are covered by the public system. Unless you ahve health problems or heriditary health problems that might kick in while you are over here, you probably don't need health insurance (I had a retinal detachment in '97 so I have insurance just in case). Check with your province; most will cover some of your expenses if you are hospitalized while abroad, and since the public system will cover you here that covers it all really. If you take medications monthly (are asthmatic, for example) get onto the drug payment scheme when you get here - you pay the forst 85 euro for drugs each month and then the rest is paid for by the state. YOu can get the app at a chemist's and you fill it out and mail it in. I think you have to go to the social welfare office and get at PPS number first (like a SIN), but that is usually pretty quick and painless, and you need that if you are going to work at all as well. If you have diabetes, you get onto the long term illness scheme and all your related drugs and supplies are covered - some other conditions are covered, like CF, but not asthma under this particular scheme. Overall, insurance isn't really necessary (unless you are really phobic about using a public hospital - I don't know what the hospitals in Dublin are like, but I would personally go jump in the Lee before I would be a patient in the South Infirmary in Cork - lovely staff, terrible building - but the Mercy is great and CUH is also good - again, with CUH excellent staff, shame about the building).
If you do decide to go with insurance, look at VHI (run by the government ) and Vivas (new company with really silly ads). I don't know if Trinity or UCD have student health centres- at UCC the GP is free if you go to the student health centre, otherwise it is around 45 euros a pop, so if there is no health centre it might be wort hgetting insurance to cover than if you go to the GP a lot.
Make sure you send your provincial health insurer a letter each year stating that you are out of the country studying; otherwise you could lose your insurance in that province.
Cheers,
M