While Roman artifacts are rare enough, they do pop up quite a lot in the Boyne Valley and all along the East Coast. It seems that the peoples of the Mediterranean were quite knowledgeable about this area during the period when Rome was a superpower. The first recorded historical reference to the Boyne was on a map in a museum in Alexandria by the philosopher Ptolemy which dates from around 150AD. This map was very accurate (even though it referred to Boyne as Buvinda) and it would have probably have been drawn by Phoenician traders.
The Roman historian, Tacitus, referred to Ireland as being easily invaded by just one legion, yet unlike the rest of Europe, there is no military or even settlement activity discovered yet.
Plenty of trade though. Apparently, the Romans were fond of our wolfhounds. Pottery dredged from the Boyne and from Collierstown have been traced back to Syria and Turkey and they were most likely used for transporting oil and wine. Artifacts found at Tara suggest that there was a Roman trading post here during the Iron Age. At the entrance to Newgrange were found high status Roman coins that were deliberatley deposited there, raising the suggestion that the mound was an international pilgrimage site for them. There was also a roman brooch found in a holywell at Randalstown which was probably another votive deposit.
Burial-wise, there are some definite Roman examples along the east coast. Cremations in Kilkenny are similar to the romano-british style from around 100AD. In Bettystown in the 70s, some very strange burials were found. They were treated differently than others in the area and with the progress in geochemistry in recent years we can tell lots more about these bodies now. Isotope analysis of their tooth enamel places this person as growing up in a very specific part of North Africa around 500AD. You have to remember that the empire was made up of a melting-pot of different ethnic groups at the time. Citizens included visitors from across the Irish Sea and they would have been quite different than the toga wearing beaurocrats we normally think about when we talk about Rome. Patrick was one of those citizens and despite the lack of traditional Roman archaeology found here, christianity was a direct import from Rome to Ireland. So the question is not what the romans have ever done for us, it is more what were they doing here while they were here.
Sources
http://de.wikipedia.org/wiki/Datei:Ptolemy_Cosmographia_1467_-_Ireland.jpg
http://www.irishtimes.com/newspaper/features/2012/1017/1224325323956.html
http://irisharchaeology.ie/2011/11/roman-contacts-with-ireland/
Raftery, B. 1994 Pagan Celtic Ireland: the enigma of the Irish Iron Age. Dublin.
Waddle, J. 1998 The Prehistoric Archaeology of Ireland, Wordwell, Dublin.