Traditions are very regional in Italy, so here is what I have grown up with since I was a little girl. Most of these "rules" belong to the North of Italy:
1 - Eat some grapes to bring you good luck! Grapes is out of season by now and it is supposed to bring good luck to those who manage to find some. Obviously now-a-days it is available most of the time as it is imported. Try to find some Italian grapes though ;-)
2 - Eat some lentils as they are supposed to bring you lots of money: the more you eat the better it is! If you never cooked lentils before, make sure you buy the precooked ones or check on the packet how long you need to put them in cold water for before cooking them. Need a recipe? Let me know!
3 - The zampone is a "must" on the table. A bit strong and greasy for some, but lovely with the lentils. I would suggest to get it from a proper butcher and ask for the cooking time.
4 - Wear some new red underwear!!! This was a typical sister-to-sister Christmas present :-) If you look in the shops you'll find plenty of "tacky" red pants and nickers with good luck messages for the new year. You can also find more refined items if you wish to spend a bit more. Just a fun tradition!
5 - Turn the radio on for the final count-down to midnight and make sure you are next to your beloved one for the first kiss of the new year!
Have fun wherever you are and may 2008 bring you all you wish for!