Controlled chaos. That is the only way I can describe the streets in Italy. From a quick glance, it would appear that they generally have the same rules of the road that we do in the US. You find cross walks everywhere, street lights, stop signs (different designs from ours), lines separating traffic, and most other things you are used to seeing. Unfortunately, if you saw this and assumed that you knew how to drive (or even walk) in Italy, you would get killed.
One of the things we determined pretty early is that cross walks are optional. Most Italians seem to either ignore them altogether, or ignore the walk/don't walk signals. Based on the other things we saw about traffic in Italy, I would have to say that most of them are playing a game of Russian Roulette where 3 of the 6 barrels are loaded. Cars and mopeds are screaming by all over the place, and finding a safe opportunity to cross can actually be somewhat difficult. This situation is made worse by some of the other rules.
At this point I need to describe the types of cars you see here. Most are extremely small by American standards. A Ford Focus is actually considered somewhat large, and an American driver would have a difficult time parking one in some parking lots. Italian drivers, on the other hand, seem to be able to parallel park in a space just 6 inches bigger than the car they are driving. Without damaging their own car or the cars around them. It is truly frightening how small of a space they can fit into.
However, more common than cars are motorcycles and mopeds (mopeds being the preferred mode of transportation around the city). There are a lot more models of moped on the road here than in all of the US, and a lot of them are actually somewhat cool (unlike the boring ones we have access to). There are some crotch-rockets as well, but very few cruisers or choppers (we saw 1 Yamaha and 1 Harley).
The utility of these mopeds becomes a lot more obvious when you see how traffic merges on streets. It appears to be a fight for position, most like in the IRL or NASCAR. I actually believe that Mario Andretti wasn't an exception driver, he just happened to grow up driving in Italy. You would routinely see people cut each other off, and nobody seemed to think anything of it. Also, it somehow seems to work, in that traffic does flow, you don't really see traffic jams, and we also didn't see any accidents. Having said that, you do start to put your seat-belt on BEFORE you tell your taxi driver where you are going, just to be safe.
Now back to traffic rules. We figured out that stop signs are also optional. No, I'm not referring to the rolling stop that most of us do at stop signs in the US, I'm saying the stop signs are just optional and a lot of people (especially mopeds) will plain ignore them. This makes cross walks that much more fun to navigate, as you constantly have to watch out for speeding Vespas when you cross. You get used to this one pretty quickly though, especially if you also learn to walk like an Italian and just ignore the cross walks.
Next, it turns out that traffic control lights are also optional. You will find a lot of people the consciously decide to ignore some lights, treating them as advisories instead of commands. This goes far beyond stragglers at a changing turn signal, and seems to be more common in the downtown areas where there are several streets terminating at the same intersection. Most commonly you will see people just make their almost-U turn or a left turn, but they are a bit more cautious than when they deal with stop signs.
Finally, lines on the road also seem to be optional. When someone wants to pass someone else, they will routinely cross over into oncoming traffic (not just empty lanes for the other direction, but actual oncoming traffic) to do so. This is probably the scariest part of how they drive, and the main reason you buckle up so quickly. Although, after writing this, I'm not so sure buckling up is such a good idea. It may be better to not buckle up so you have the option to jump out.
Now, after having written all of this, you might think that we took cabs quite often while in Italy. That is actually extremely far from the truth. We actually rarely used them (typically only to/from the train station to the hotel and getting back to the hotel on the first night in a given city). The cities are actually relatively compact so you can walk to most places (this includes Rome). By our estimates, we walked about 60 to 70 miles during the 10 days we were in Italy. Our calves did get a little sore after the Cinque Terre hike (7 miles of very hilly terrain), but overall we were fine.
As another anecdote, we also saw an H2 parked on the street. Compared to all of the other cars on the road it looked like Eisenhower had decided to drive some tanks into Rome.