Use an adapter when the plug configuration of your device does not match the receptacle you are plugging into. Any US device with two flat prongs will not insert into an Italian receptacle, which requires two round prongs.
Use a converter or transformer to step-down 220v European current to match the 110v of your US device, or depending on the type, step-up the 110v requirement of your device to match the 220v European current.
Converters are used with simple heating devices, such as irons, hair dryers and curling irons. They should not be used with devices containing electronic circuitry, curling irons over 25 watts, or devices with ground fault protectors.
Transformers are for devices with electronic circuitry, such as computers, CD players, etc.
Converters and transformers are inconveniently heavy to include in your carry-on or checked baggage. And, they are totally unnecessary if your have dual voltage (110/220v) devices. Most all electronic devices made today for travel (computers, battery chargers, iPads, iPods, etc.) are dual voltage. Many curling irons and hair dryers are also dual voltage, some with a switch setting and others built in. Check the specifications printed or embossed on your devices to see if the input required says something like 100v - 240v. Or, contact the manufacturer. If so, they are dual voltage.
If a device is not dual voltage, I would replace it with one that is rather than lugging a converter/transformer. Following is a link to a web site that may be helpful to view the array of various devices available. Conair is a familiar manufacturer but I have never used their web site. These devices are all readily available elsewhere.