Celtic to the End
The Romans never saw a land they didn't want to conquer, but they never conquered Ireland. Julius Caesar initiated contact with Britain in 55 B.C.E., and for over a century the Romans planned to conquer the whole island. Though some Britons became Romanized, many locals didn't appreciate being colonized and fought their conquerors tooth and nail.
The Romans couldn't keep enough troops on the island to hold them at bay. They had other frontiers to guard, after all. By 122 C.E., Hadrian had decided it would be wise to wall off Scotland to keep the barbarians separate from Romanized territory. Over the next two centuries, Rome gradually lost control over Britain.
The Romans knew Ireland existed; Ireland's Latin name is Hibernia, which might mean “Land of Winter.” (Another theory holds that it comes from Iberia, or Spain.) Julius Caesar mentioned Ireland in his Commentaries, but just to note that it was less than half the size of Britain. The Greek geographer Strabo claimed that Ireland was on the edge of habitable earth and that the inhabitants of the island were complete savages living a miserable existence due to the cold climate.
Some “experts” thought Ireland must be some sort of El Dorado, a land of fabulous wealth. Solinus, writing in the third century C.E., claimed that Ireland's grass was so rich that Irish cows regularly exploded from eating too much of it. He also noted that there were no snakes in Ireland, which probably made St. Patrick's job a lot easier when he arrived in the next century.
The Roman Tacitus, writing around 100 C.E., thought Ireland was very much like Britain. In the late first century C.E., Agricola, a Roman governor of Britain, considered conquering Ireland and even did reconnaissance; he decided that the Romans could take the island with just one legion of soldiers, but it probably wouldn't be worth the effort.
But the Romans never tried to conquer Ireland. The distance from Rome was too great and the potential payoff too uncertain, and they already had their hands full with Britain. And so the Irish remained Celtic.

