Rome can be absolutely mentioned as one of the best shopping paradises worldwide. Here in fact you can find everything you need, from clothes to souvenirs, to every kind of stuff.
Go to the historical city-centre and find out some of the most lovely boutiques you'll ever see : from high fashion's boutiques to hand-crafted and handmade-pieces-selling ones, your shopping experience will be amazing like no other. Via del Boschetto, Via dei Condotti, Via del Babuino, Via Frattina, are just some of the most famous streets where to do a very glamour (and quite expensive as well...;) shopping.
Otherwise, if you're looking for a mass and undifferenitated shopping, keep in mind that Rome has been growing so fastly since a couple of years in terms of big shopping malls : Parco Leonardo is probably the best example for who's seeking this kind experience... Located near the International Airport "Leonardo da Vinci", Parco Leonardo also hosts, beyond around 100 shops, one of the biggest cinema in the whole Italy.
Other important shopping malls in Rome are : Centro Commerciale Anagnina, Le RoyMerlin (all intended for bricolage and do-it-yourselfers), Centro Commerciale Lunghezza, Centro Commerciale Cinecittà 2, and many more. Here all the main brands of every market sector have their own shop.