Italian Souvenirs

Leather (very helpful post on choosing Italian leather)
Magnets, key chains, miniature ceramics, statues of sites, post cards
Moor jewelry

Kitchen: oven mitts, towels, espresso mugs, coffee cups, placemats
olive tree cutting boards or salad bowls/spoons

Italian Specialties:
Most of these items you can find throughout Italy, but I've listed where they are a specialty.
Leather (Florence)
Blown glass (Venice)
Woodwork (Dolomites)
Nativity Scenes (Naples)
Pinocchio (Lucca)
Silk (Como)
Ceramics (Sicily)
Pesto (Liguria)
Truffles (Tuscany)
Cantucci Biscuits (Siena)
Parmesan (Parma)
Tablecloths (Perugia)
Chocolate (Modica)

Wine - every region has it's treasures
Limoncello - intensely lemon-flavored liqueur most famously associated with and produced in Sorrento, the Amalfi coast, and the island of Capri
Grappa - popular alcoholic drink; The main ingredient of grappa is pomace, which consists of the grape skins, seeds and stalks that are left over from the winemaking process. These are taken through a second process of distillation, which extracts the remaining flavours from the pomace before the waste is discarded. The grappa is then either bottled at once, which creates white grappa (grappa bianca), or aged in wooden casks to create the yellow or brown-hued grappa known as riserva.
Sambuca - anise-flavoured, usually colourless, liqueur created in Civitavecchia, a port city north of Rome
Amaro - Amaro Montenegro is a traditional amaro distilled in Bologna, Italy. Amaro Lucano S.p.A., a family-owned company based in Pisticci, Basilicata.
Prosecco - is not champagne. The name Prosecco is derived from the Italian village of Prosecco near Trieste, where the grape and wine is said to have originated. Prosecco DOC is produced in nine provinces spanning the Venetoand Friuli Venezia Giulia regions.
Campari - an alcoholic liqueur, considered an apéritif. It is a bitters obtained from the infusion of herbs and fruit. Invented in Novara, Italy, it is popular in the north and especially Milan. 

Kiko makeup
Rose tonic water
Umbrian clay
Nivea cream (little blue tin)
And here's a short review of a few of my favorite Italian beauty products.

Food Products:
Porcini mushrooms (so good in risotto!!)
Sundried tomatoes
Balsamic vinegar
Olive Oils and Olives
Pasta in different shapes/colors
Pesto, Bruschetta spreads
Tuna stuffed red peppers
Truffle anything
Lavazza coffee or Pocket Coffee
Parmesan or other dried cheeses
Cookies (biscotti, spumoni, amaretti, torrone, Mulino Bianco is a famous brand)
Kinder goodies
Lemon candies and limoncello almonds
Spice mixes and dried sauce mixes (you can find these in little tins too)
Taralli (Puglia)
Amarena cherries
Cantucci biscuits

Prayer cards