Bring clothes obviously - not your entire wardrobe, but the things you wear most in the winter and summer - same goes for shoes. I'd bring more clothes than anything else because personally I find shopping here isn't great. Everything's way too expensive for the quality of material you get. Bring toiletries and personal brands you like (i.e. if you're in Dublin and like Crest toothpaste, bring it cuz they don't sell Crest here although I heard they sell it in Galway...). Don't bring bedding (towels/sheets,etc.) because you can buy them here.
I would not bring books - maybe 1 or 2 that you've found either cheaper in the US (like off ebay or amazon used or something) or that have helped you understand basic sciences. Electronics, if you use them heavily, are ok (laptop, md/mp3 player, digital camera, even cd burner if you've got that kind of thing and use it). I wouldn't bring that many valuables because airport security cut locks to check bags and I've had things stolen from my luggage before by airport people. Make sure you have 1 heavy duty electronics voltage converter.
to create more space, you can get those vacuum bags to put your clothes in that sucks all the air out.
Really, Irish stuff isn't really different from American stuff, you can buy what you need here. But in some cases, it may be slightly more expensive. The foreign exchange rate is dropping in our favor, but is still more favorable to the euro.
